Pub Date : 2026-01-07DOI: 10.1016/j.chaos.2026.117873
Fang Li, Huiwen Wang
It is hard to get analytical solutions for nonlinear fractional differential equations with variable coefficients. Standard methods like the Laplace transform and iterative techniques often do not work well for these problems. In this work, we construct an explicit representation of the Green function for nonlinear fractional differential equations and find analytical solutions to the above equations in weighted spaces. As applications of our results, we present explicit solutions to fractional oscillation equations, logistic equations, Riccati equations with initial conditions.
{"title":"Constructions of analytical solutions to nonlinear fractional differential equations with variable coefficients","authors":"Fang Li, Huiwen Wang","doi":"10.1016/j.chaos.2026.117873","DOIUrl":"10.1016/j.chaos.2026.117873","url":null,"abstract":"<div><div>It is hard to get analytical solutions for nonlinear fractional differential equations with variable coefficients. Standard methods like the Laplace transform and iterative techniques often do not work well for these problems. In this work, we construct an explicit representation of the Green function for nonlinear fractional differential equations and find analytical solutions to the above equations in weighted spaces. As applications of our results, we present explicit solutions to fractional oscillation equations, logistic equations, Riccati equations with initial conditions.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117873"},"PeriodicalIF":5.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-07DOI: 10.1016/j.chaos.2025.117791
Ramen Ghosh
Sparse neural networks often match the performance of dense models until a sharp pruning level is crossed, after which trainability and generalization collapse abruptly—a hallmark of a non-equilibrium phase transition in a complex system. Existing explanations based on static connectivity (e.g., expansion or Ramanujan properties) overlook the stochastic, time-dependent nature of learning dynamics. We recast pruning+training as a random dynamical system driven by a sequence of stochastic update operators and analyze its Lyapunov spectrum and associated spectral entropy as physically meaningful order parameters. This viewpoint yields a mechanism-level account of when sparsity preserves stability and when it fails.
Our contributions are threefold: (i) we prove the existence of a critical sparsity at which spectral stability is lost — identified by a qualitative change in the Lyapunov spectrum and a collapse of spectral entropy — explaining the observed performance cliff; (ii) we establish a spectral large-deviations principle that quantifies fluctuations of test error via the spectrum of the training cocycle, predicting finite-size effects and metastability windows; and (iii) we formulate pruning as an ergodic control problem, showing that Gibbs-type policies implement an explicit energy–entropy trade-off that preserves statistically steady behavior under stochastic updates. Stylized cocycle simulations and a small synthetic neural-network experiment assist the theory by visualizing spectral mass collapse, hysteresis near the threshold, and the limits of expansion-based heuristics. The results place sparse learning within a broader non-equilibrium framework — linking spectral thermodynamics, phase transitions in complex networks, and self-organization — while keeping mathematical details in appendices for accessibility.
{"title":"Non-equilibrium spectral thermodynamics of pruning: Phase transitions in sparse neural networks","authors":"Ramen Ghosh","doi":"10.1016/j.chaos.2025.117791","DOIUrl":"10.1016/j.chaos.2025.117791","url":null,"abstract":"<div><div>Sparse neural networks often match the performance of dense models until a sharp pruning level is crossed, after which trainability and generalization collapse abruptly—a hallmark of a non-equilibrium phase transition in a complex system. Existing explanations based on static connectivity (e.g., expansion or Ramanujan properties) overlook the stochastic, time-dependent nature of learning dynamics. We recast pruning+training as a random dynamical system driven by a sequence of stochastic update operators and analyze its <em>Lyapunov spectrum</em> and associated <em>spectral entropy</em> as physically meaningful order parameters. This viewpoint yields a mechanism-level account of when sparsity preserves stability and when it fails.</div><div>Our contributions are threefold: (i) we prove the existence of a <em>critical sparsity</em> at which spectral stability is lost — identified by a qualitative change in the Lyapunov spectrum and a collapse of spectral entropy — explaining the observed performance cliff; (ii) we establish a <em>spectral large-deviations principle</em> that quantifies fluctuations of test error via the spectrum of the training cocycle, predicting finite-size effects and metastability windows; and (iii) we formulate pruning as an <em>ergodic control</em> problem, showing that Gibbs-type policies implement an explicit energy–entropy trade-off that preserves statistically steady behavior under stochastic updates. Stylized cocycle simulations and a small synthetic neural-network experiment <em>assist</em> the theory by visualizing spectral mass collapse, hysteresis near the threshold, and the limits of expansion-based heuristics. The results place sparse learning within a broader non-equilibrium framework — linking spectral thermodynamics, phase transitions in complex networks, and self-organization — while keeping mathematical details in appendices for accessibility.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117791"},"PeriodicalIF":5.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-07DOI: 10.1016/j.chaos.2025.117857
Guanghan Peng , Yanhong Xia , Shuhong Yang , Chenchen Lu , Huili Tan , Dongxue Xia
In recent years, overtaking behavior has become a major cause of traffic accidents, not only leading to unstable traffic flow but also affecting transportation efficiency and driving safety. With the rapid development of connected autonomous vehicles (CAVs), the heterogeneous traffic flow model composed of CAVs and human-driven vehicles (HDVs) has gradually become the mainstream traffic configuration. To mitigate the instability caused by overtaking in heterogeneous traffic flows, we in this study establish a novel heterogeneous macro continuum model, focusing on analyzing the impact of multi-source integrated information including overtaking, lateral clearance, electronic throttle angle, and CAVs penetration rate on system stability. Through theoretical analysis using linear stability methods and nonlinear perturbation techniques, the neutral stability conditions and KdV-Burgers equation for this new heterogeneous continuum model are derived. Moreover, numerical simulations reveal the quantitative impacts of key parameters: Firstly, by increasing the overtaking coefficient φ from 0 to 0.15, the density wave amplitude is significantly amplified from 0.0574 veh/m to 0.0967 veh/m with a 68.5 % increase, which shows that the overtaking highlights its strong destabilizing effect. Secondly, density fluctuations are effectively suppressed from approximately 0.0597 veh/m to 0.0477 veh/m with a 20.1 % decrease due to increasing the lateral gap coefficient k from 0.1 to 0.3. Simultaneously, the density wave amplitude decreases from 0.0618 veh/m to 0.0508 veh/m with a 17.8 % reduction owing to enhancing the ETAD coefficient γ from 0 to 0.6, which improves system damping and slows disturbance propagation. Finally, the density wave amplitude is reduced from 0.0631 veh/m to 0.0511 veh/m with a 19.0 % decrease by increasing the CAVs penetration rate p from 0.2 to 0.8, effectively suppressing the development of stop-and-go waves and shrinking the phase trajectory limit cycle area. Above results demonstrate that the comprehensive application of multi-source information, particularly maintaining appropriate lateral gap, increasing the coefficient of ETAD and CAVs penetration rates, can significantly enhance the stability of mixed traffic flows, alleviate congestion, and improve road capacity and overall traffic efficiency although overtaking inherently tends to destabilize.
{"title":"Phase transition of multi-source information-integrated macroscopic continuum model under heterogeneous vehicles environment","authors":"Guanghan Peng , Yanhong Xia , Shuhong Yang , Chenchen Lu , Huili Tan , Dongxue Xia","doi":"10.1016/j.chaos.2025.117857","DOIUrl":"10.1016/j.chaos.2025.117857","url":null,"abstract":"<div><div>In recent years, overtaking behavior has become a major cause of traffic accidents, not only leading to unstable traffic flow but also affecting transportation efficiency and driving safety. With the rapid development of connected autonomous vehicles (CAVs), the heterogeneous traffic flow model composed of CAVs and human-driven vehicles (HDVs) has gradually become the mainstream traffic configuration. To mitigate the instability caused by overtaking in heterogeneous traffic flows, we in this study establish a novel heterogeneous macro continuum model, focusing on analyzing the impact of multi-source integrated information including overtaking, lateral clearance, electronic throttle angle, and CAVs penetration rate on system stability. Through theoretical analysis using linear stability methods and nonlinear perturbation techniques, the neutral stability conditions and KdV-Burgers equation for this new heterogeneous continuum model are derived. Moreover, numerical simulations reveal the quantitative impacts of key parameters: Firstly, by increasing the overtaking coefficient φ from 0 to 0.15, the density wave amplitude is significantly amplified from 0.0574 veh/m to 0.0967 veh/m with a 68.5 % increase, which shows that the overtaking highlights its strong destabilizing effect. Secondly, density fluctuations are effectively suppressed from approximately 0.0597 veh/m to 0.0477 veh/m with a 20.1 % decrease due to increasing the lateral gap coefficient k from 0.1 to 0.3. Simultaneously, the density wave amplitude decreases from 0.0618 veh/m to 0.0508 veh/m with a 17.8 % reduction owing to enhancing the ETAD coefficient γ from 0 to 0.6, which improves system damping and slows disturbance propagation. Finally, the density wave amplitude is reduced from 0.0631 veh/m to 0.0511 veh/m with a 19.0 % decrease by increasing the CAVs penetration rate p from 0.2 to 0.8, effectively suppressing the development of stop-and-go waves and shrinking the phase trajectory limit cycle area. Above results demonstrate that the comprehensive application of multi-source information, particularly maintaining appropriate lateral gap, increasing the coefficient of ETAD and CAVs penetration rates, can significantly enhance the stability of mixed traffic flows, alleviate congestion, and improve road capacity and overall traffic efficiency although overtaking inherently tends to destabilize.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117857"},"PeriodicalIF":5.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145921919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-07DOI: 10.1016/j.chaos.2025.117746
Evan O’Riordan, Frank G. Glavin, Colm O’Riordan
In this paper, we investigate the emergence of fairness in a dynamic network where agents play the Dictator Game. Agents are initially positioned on a regular lattice graph and interact as both dictators and recipients while updating their trust relationships via weights. If trust values are low, agents can potentially sever connections and randomly establish new links, dynamically reshaping the network topology. We demonstrate how this adaptive rewiring mechanism leads to the emergence of fair and generous clusters. Our findings reveal that the combination of trust updating and selective rewiring promotes higher levels of fairness than those observed in static networks, with implications for understanding the evolution of cooperative behaviour in social and economic systems.
{"title":"Rewiring to promote fairness in the Dictator Game","authors":"Evan O’Riordan, Frank G. Glavin, Colm O’Riordan","doi":"10.1016/j.chaos.2025.117746","DOIUrl":"10.1016/j.chaos.2025.117746","url":null,"abstract":"<div><div>In this paper, we investigate the emergence of fairness in a dynamic network where agents play the Dictator Game. Agents are initially positioned on a regular lattice graph and interact as both dictators and recipients while updating their trust relationships via weights. If trust values are low, agents can potentially sever connections and randomly establish new links, dynamically reshaping the network topology. We demonstrate how this adaptive rewiring mechanism leads to the emergence of fair and generous clusters. Our findings reveal that the combination of trust updating and selective rewiring promotes higher levels of fairness than those observed in static networks, with implications for understanding the evolution of cooperative behaviour in social and economic systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117746"},"PeriodicalIF":5.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-07DOI: 10.1016/j.chaos.2026.117865
Joydeep Das, Abhishek Chaudhuri, Sudeshna Sinha
We explore pattern formation in an active fluid system involving two chemical species that regulate active stress: a fast-diffusing species () and a slow-diffusing species (). The growth of species is modelled using a nonlinear logistic term. Through linear stability analysis, we derive phase diagrams illustrating the various dynamical regimes in parameter space. Our findings indicate that an increase in the Péclet number results in the destabilization of the uniform steady state. In contrast, counter-intuitively, an increase in the nonlinear growth parameter of actually stabilizes the homogeneous steady-state regime. Additionally, we observe that greater asymmetry between the species leads to three distinct dynamical phases, while low asymmetry fails to produce oscillatory instability. Numerical simulations conducted in instability regimes show patterns that range from irregular, arrhythmic configurations at high Péclet numbers to both transient and robust symmetry-breaking chimera states. Notably, these chimera patterns are more prevalent in the oscillatory instability regime, and our stability analysis indicates that this regime is the most extensive for high nonlinear growth parameters and moderately high Péclet numbers. Further, we also find soliton-like structures where aggregations of species merge, and new aggregations spontaneously emerge, and these patterns are prevalent in the phase of stationary instability. Overall, our study illustrates that a diverse array of patterns can emerge in active matter influenced by nonlinear growth in a chemical species, with chimeras being particularly dominant when the nonlinear growth parameter is elevated.
{"title":"From order to chimeras: Unravelling dynamic patterns in active fluids with nonlinear growth","authors":"Joydeep Das, Abhishek Chaudhuri, Sudeshna Sinha","doi":"10.1016/j.chaos.2026.117865","DOIUrl":"10.1016/j.chaos.2026.117865","url":null,"abstract":"<div><div>We explore pattern formation in an active fluid system involving two chemical species that regulate active stress: a fast-diffusing species (<span><math><mi>A</mi></math></span>) and a slow-diffusing species (<span><math><mi>I</mi></math></span>). The growth of species <span><math><mi>A</mi></math></span> is modelled using a nonlinear logistic term. Through linear stability analysis, we derive phase diagrams illustrating the various dynamical regimes in parameter space. Our findings indicate that an increase in the Péclet number results in the destabilization of the uniform steady state. In contrast, counter-intuitively, an increase in the nonlinear growth parameter of <span><math><mi>A</mi></math></span> actually stabilizes the homogeneous steady-state regime. Additionally, we observe that greater asymmetry between the species leads to three distinct dynamical phases, while low asymmetry fails to produce oscillatory instability. Numerical simulations conducted in instability regimes show patterns that range from irregular, arrhythmic configurations at high Péclet numbers to both transient and robust symmetry-breaking chimera states. Notably, these chimera patterns are more prevalent in the oscillatory instability regime, and our stability analysis indicates that this regime is the most extensive for high nonlinear growth parameters and moderately high Péclet numbers. Further, we also find soliton-like structures where aggregations of species <span><math><mi>A</mi></math></span> merge, and new aggregations spontaneously emerge, and these patterns are prevalent in the phase of stationary instability. Overall, our study illustrates that a diverse array of patterns can emerge in active matter influenced by nonlinear growth in a chemical species, with chimeras being particularly dominant when the nonlinear growth parameter is elevated.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117865"},"PeriodicalIF":5.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-07DOI: 10.1016/j.chaos.2025.117781
Huiqin Shu , Shaohua Luo , Dahui Luo , Le Zheng , Hassen M. Ouakad
This paper investigates dynamical analysis and predefined finite-time backstepping control for a small network consisting four coupled MEMS resonators. Firstly, a novel small network structure of coupled MEMS resonators is proposed to enhance sensitivity and bandwidth, and its corresponding mathematical model is established. Secondly, a detailed dynamic analysis is conducted to examine the influence of system parameters, including the applied alternating voltage, on the system's behavior. The results reveal that chaotic oscillations become more severe as the applied alternating voltage increases a little or exceeds a critical coupling threshold. Thirdly, to suppress these detrimental chaotic oscillations and simultaneously achieve high-performance control, a predefined finite-time backstepping control strategy is developed. The approach incorporates a predefined performance function to transform the state-constraint problem into a boundedness problem involving newly defined variables. A type-2 sequential fuzzy neural network (T2SFNN) is used to approximate unknown nonlinear functions, and an improved accelerated exponential integral tracking differentiator (AEITD) is employed to resolve the differential explosion issue in the backstepping design. Rigorous stability analysis confirms that all closed-loop signals remain bounded and the tracking errors stay within a prescribed range. Finally, extensive simulation results demonstrate the feasibility, robustness and superiority of the proposed approach.
{"title":"Dynamical analysis and predefined finite-time backstepping control for a small network consisting four coupled MEMS resonators","authors":"Huiqin Shu , Shaohua Luo , Dahui Luo , Le Zheng , Hassen M. Ouakad","doi":"10.1016/j.chaos.2025.117781","DOIUrl":"10.1016/j.chaos.2025.117781","url":null,"abstract":"<div><div>This paper investigates dynamical analysis and predefined finite-time backstepping control for a small network consisting four coupled MEMS resonators. Firstly, a novel small network structure of coupled MEMS resonators is proposed to enhance sensitivity and bandwidth, and its corresponding mathematical model is established. Secondly, a detailed dynamic analysis is conducted to examine the influence of system parameters, including the applied alternating voltage, on the system's behavior. The results reveal that chaotic oscillations become more severe as the applied alternating voltage increases a little or exceeds a critical coupling threshold. Thirdly, to suppress these detrimental chaotic oscillations and simultaneously achieve high-performance control, a predefined finite-time backstepping control strategy is developed. The approach incorporates a predefined performance function to transform the state-constraint problem into a boundedness problem involving newly defined variables. A type-2 sequential fuzzy neural network (T2SFNN) is used to approximate unknown nonlinear functions, and an improved accelerated exponential integral tracking differentiator (AEITD) is employed to resolve the differential explosion issue in the backstepping design. Rigorous stability analysis confirms that all closed-loop signals remain bounded and the tracking errors stay within a prescribed range. Finally, extensive simulation results demonstrate the feasibility, robustness and superiority of the proposed approach.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117781"},"PeriodicalIF":5.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145921929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A hybrid fluid-kinetic (statistical mechanical) approach is adopted to model the dynamics of solitary waves representing collective ion excitations in a plasma contaminated with massive charged dust particulates. The ion component is modeled by fluid-dynamical equations, while the background electron population is modeled by a statistical–mechanical (i.e., kinetic) formalism. A multi-scale (reductive perturbation) technique reduces the fluid-kinetic formulation to a modified Korteweg–de Vries (KdV) equation, incorporating an additional term associated to kinetic effects, leading to wave damping. Our aim is to trace the combined influence of the charged dust concentration on the collisionless kinetic damping (known as Landau damping) mechanism affecting electrostatic waves propagating in a plasma contaminated by charged dust particulates (commonly referred to as a dusty plasma). A kappa-type distribution is assumed for the electrons, in agreement with Space observations. As a striking new aspect in this study, solitary wave polarity reversal is predicted when the dust concentration exceeds a certain threshold; this is true regardless of the kappa parameter value. The dependence of the damped solitary wave propagation characteristics on the (non-Maxwellian) electron statistics and on the dust concentration has been investigated.
{"title":"Damped Korteweg–de Vries equation in a fluid-kinetic model for dusty plasmas","authors":"Hadia Mushtaq , Kuldeep Singh , Sadia Zaheer , Ioannis Kourakis","doi":"10.1016/j.chaos.2026.117870","DOIUrl":"10.1016/j.chaos.2026.117870","url":null,"abstract":"<div><div>A hybrid fluid-kinetic (statistical mechanical) approach is adopted to model the dynamics of solitary waves representing collective ion excitations in a plasma contaminated with massive charged dust particulates. The ion component is modeled by fluid-dynamical equations, while the background electron population is modeled by a statistical–mechanical (i.e., kinetic) formalism. A multi-scale (reductive perturbation) technique reduces the fluid-kinetic formulation to a modified Korteweg–de Vries (KdV) equation, incorporating an additional term associated to kinetic effects, leading to wave damping. Our aim is to trace the combined influence of the charged dust concentration on the collisionless kinetic damping (known as Landau damping) mechanism affecting electrostatic waves propagating in a plasma contaminated by charged dust particulates (commonly referred to as a dusty plasma). A kappa-type distribution is assumed for the electrons, in agreement with Space observations. As a striking new aspect in this study, solitary wave polarity reversal is predicted when the dust concentration exceeds a certain threshold; this is true regardless of the kappa parameter value. The dependence of the damped solitary wave propagation characteristics on the (non-Maxwellian) electron statistics and on the dust concentration has been investigated.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117870"},"PeriodicalIF":5.6,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-06DOI: 10.1016/j.chaos.2025.117850
Yuejuan Xu , Youjun Liu , Bao Li , Tongna Wang , Zichang Wang , Qingqing Guan , Gerold Baier , Denggui Fan , Liyuan Zhang , Jinping Dong
Epilepsy is a common neurological disorder whose pathogenesis involves dysfunction in neurovascular coupling. However, current models still lack sufficient realism and diversity. This study investigates the pathological mechanisms of epilepsy based on the physiological process of neurovascular coupling. Our mathematical model incorporates neurons, astrocytes, and arterioles. It employs an extended Hodgkin–Huxley-type model for neuronal dynamics and a model of radius variation in smooth muscle driven by the filament sliding mechanism. Key elements such as and potassium channels, along with signaling molecules including , and , are integrated to simulate neuro-hemodynamic responses. The results reveal six distinct transitional firing patterns in neurons under a suitable external stimulation, along with bifurcation phenomena underlying the low-voltage fast oscillation state, tonic spiking, and bursting. Both qualitative and quantitative simulations demonstrate that neuronal activation triggers oscillatory calcium waves in astrocytes, leading to the release of vasodilators and ultimately inducing arteriole dilation. Furthermore, the study delineates the asymptotic behaviors of ionic concentration changes under conditions of ischemia, hypoxia, and astrocytic dysfunction. This multi-pathway synergistic neurovascular coupling framework provides a more comprehensive understanding of epileptic pathology.
{"title":"Deciphering epileptic dynamics through neurovascular coupling: Insights from a neuro-astrocytic-arteriolar computational modeling approach","authors":"Yuejuan Xu , Youjun Liu , Bao Li , Tongna Wang , Zichang Wang , Qingqing Guan , Gerold Baier , Denggui Fan , Liyuan Zhang , Jinping Dong","doi":"10.1016/j.chaos.2025.117850","DOIUrl":"10.1016/j.chaos.2025.117850","url":null,"abstract":"<div><div>Epilepsy is a common neurological disorder whose pathogenesis involves dysfunction in neurovascular coupling. However, current models still lack sufficient realism and diversity. This study investigates the pathological mechanisms of epilepsy based on the physiological process of neurovascular coupling. Our mathematical model incorporates neurons, astrocytes, and arterioles. It employs an extended Hodgkin–Huxley-type model for neuronal dynamics and a model of radius variation in smooth muscle driven by the filament sliding mechanism. Key elements such as <span><math><mi>BK</mi></math></span> and <span><math><mi>KIR</mi></math></span> potassium channels, along with signaling molecules including <span><math><msub><mi>O</mi><mn>2</mn></msub></math></span>, <span><math><mi>C</mi><msup><mi>a</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></math></span>and <span><math><mi>NO</mi></math></span>, are integrated to simulate neuro-hemodynamic responses. The results reveal six distinct transitional firing patterns in neurons under a suitable external stimulation, along with bifurcation phenomena underlying the low-voltage fast oscillation state, tonic spiking, and bursting. Both qualitative and quantitative simulations demonstrate that neuronal activation triggers oscillatory calcium waves in astrocytes, leading to the release of vasodilators and ultimately inducing arteriole dilation. Furthermore, the study delineates the asymptotic behaviors of ionic concentration changes under conditions of ischemia, hypoxia, and astrocytic dysfunction. This multi-pathway synergistic neurovascular coupling framework provides a more comprehensive understanding of epileptic pathology.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117850"},"PeriodicalIF":5.6,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-06DOI: 10.1016/j.chaos.2025.117813
Tolga Omay , Dumitru Baleanu
This paper introduces the First-Order Fractional Differencing (FOFD) operator that substantially reduces the computational burden of fractional differencing for large-scale applications. While the standard Grünwald–Letnikov (GL) operator requires operations for a series of length , and recent FFT-based methods achieve , our FOFD operator requires only operations through a simple two-point recursion. We develop an optimal weight calibration framework that ensures this computational efficiency does not compromise statistical accuracy, deriving a general formula that adapts to the persistence structure of autoregressive processes. Empirical applications demonstrate substantial improvements: for the Chicago Fed National Financial Conditions Index with extreme persistence (), optimal weight calibration reduces approximation error by 93% while preserving the autocorrelation structure of the GL operator. For a series of 10,000 observations, our method requires 20,000 operations compared to 530,000 for FFT-based methods and 50 million for standard implementations—enabling fractional differencing in real-time and high-frequency contexts previously infeasible due to computational constraints. The method’s simplicity, requiring no specialized libraries and providing direct implementation through our calibration formula, makes it immediately accessible to practitioners while maintaining the long-memory properties essential for financial time series modeling.
{"title":"A computationally efficient approximation for fractional differencing: First-order operators","authors":"Tolga Omay , Dumitru Baleanu","doi":"10.1016/j.chaos.2025.117813","DOIUrl":"10.1016/j.chaos.2025.117813","url":null,"abstract":"<div><div>This paper introduces the First-Order Fractional Differencing (FOFD) operator that substantially reduces the computational burden of fractional differencing for large-scale applications. While the standard Grünwald–Letnikov (GL) operator requires <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> operations for a series of length <span><math><mi>T</mi></math></span>, and recent FFT-based methods achieve <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>T</mi><mo>log</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span>, our FOFD operator requires only <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>T</mi><mo>)</mo></mrow></mrow></math></span> operations through a simple two-point recursion. We develop an optimal weight calibration framework that ensures this computational efficiency does not compromise statistical accuracy, deriving a general formula <span><math><mrow><msub><mrow><mi>w</mi></mrow><mrow><mtext>opt</mtext></mrow></msub><mo>=</mo><mi>d</mi><mi>⋅</mi><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mn>0</mn><mo>.</mo><mn>9</mn><mi>ρ</mi><mo>)</mo></mrow></mrow><mrow><mi>β</mi><mrow><mo>(</mo><mi>p</mi><mo>)</mo></mrow></mrow></msup></mrow></math></span> that adapts to the persistence structure of autoregressive processes. Empirical applications demonstrate substantial improvements: for the Chicago Fed National Financial Conditions Index with extreme persistence (<span><math><mrow><mi>ρ</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>992</mn></mrow></math></span>), optimal weight calibration reduces approximation error by 93% while preserving the autocorrelation structure of the GL operator. For a series of 10,000 observations, our method requires 20,000 operations compared to 530,000 for FFT-based methods and 50 million for standard implementations—enabling fractional differencing in real-time and high-frequency contexts previously infeasible due to computational constraints. The method’s simplicity, requiring no specialized libraries and providing direct implementation through our calibration formula, makes it immediately accessible to practitioners while maintaining the long-memory properties essential for financial time series modeling.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117813"},"PeriodicalIF":5.6,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145922002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-06DOI: 10.1016/j.chaos.2025.117851
Bingxu Min, Gang Xiong
The singularity power spectrum (SPS) characterizes the energy distribution of signals through a power measure defined in the singularity exponent domain. However, existing SPS methods are restricted to univariate analysis and cannot capture the joint energy distribution of multichannel signals in a unified singularity exponent space. To overcome this limitation and inspired by the dimensional joint analysis framework of the multivariate multifractal spectrum (MV-MFS), this paper proposes—to the best of our knowledge—the first formulation of a bivariate singularity power spectrum (BV-SPS) and its generalization, the multivariate singularity power spectrum (MV-SPS). The theoretical definition and model of MV-SPS are established by extending the conventional SPS framework. Taking the bivariate case as an illustrative example, we detail the algorithmic implementation, which involves constructing two-dimensional joint singularity subsets and estimating the bivariate joint power spectrum using a geometric-mean power measure. The approach is then generalized to the multivariate case through the construction of high-dimensional joint singularity subsets and the introduction of a multivariate geometric-mean power function, thereby enabling the characterization of energy-distribution features across multiple signals in a unified high-dimensional singularity exponent space. Experimental validation on the IPIX radar dataset demonstrates the superior performance of the proposed MV-SPS in sea-clutter classification and low-resolution weak-target detection. This study establishes a novel technical pathway for multidimensional information fusion, target feature extraction, and detection/recognition based on fractal-domain signal analysis.
{"title":"Multivariate singularity power spectrum distribution and its application to radar target detection","authors":"Bingxu Min, Gang Xiong","doi":"10.1016/j.chaos.2025.117851","DOIUrl":"10.1016/j.chaos.2025.117851","url":null,"abstract":"<div><div>The singularity power spectrum (SPS) characterizes the energy distribution of signals through a power measure defined in the singularity exponent domain. However, existing SPS methods are restricted to univariate analysis and cannot capture the joint energy distribution of multichannel signals in a unified singularity exponent space. To overcome this limitation and inspired by the dimensional joint analysis framework of the multivariate multifractal spectrum (MV-MFS), this paper proposes—to the best of our knowledge—the first formulation of a bivariate singularity power spectrum (BV-SPS) and its generalization, the multivariate singularity power spectrum (MV-SPS). The theoretical definition and model of MV-SPS are established by extending the conventional SPS framework. Taking the bivariate case as an illustrative example, we detail the algorithmic implementation, which involves constructing two-dimensional joint singularity subsets and estimating the bivariate joint power spectrum using a geometric-mean power measure. The approach is then generalized to the multivariate case through the construction of high-dimensional joint singularity subsets and the introduction of a multivariate geometric-mean power function, thereby enabling the characterization of energy-distribution features across multiple signals in a unified high-dimensional singularity exponent space. Experimental validation on the IPIX radar dataset demonstrates the superior performance of the proposed MV-SPS in sea-clutter classification and low-resolution weak-target detection. This study establishes a novel technical pathway for multidimensional information fusion, target feature extraction, and detection/recognition based on fractal-domain signal analysis.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"205 ","pages":"Article 117851"},"PeriodicalIF":5.6,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145921921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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