Pub Date : 2026-07-01Epub Date: 2026-02-24DOI: 10.1016/j.chaos.2026.118138
Zohra Mehri , Abdelâali Boudjemâa
We study Anderson localization of a one-dimensional quantum droplet in a speckle-like potential employing the generalized Gross–Pitaevskii equation. We compute the droplet width, density profiles, diffusion exponent and coefficient, and the localization length for both small and large droplets. Interesting classes of anomalous diffusions are obtained in transport dynamics ranging from superdiffusion to subdiffusion for a strong disorder strength. We find that above a certain critical disorder strength the droplet exhibits a transition to Anderson localization on the tails. Our results can be readily probed with recent experiments.
{"title":"Anderson localization of quantum droplets in disordered potentials","authors":"Zohra Mehri , Abdelâali Boudjemâa","doi":"10.1016/j.chaos.2026.118138","DOIUrl":"10.1016/j.chaos.2026.118138","url":null,"abstract":"<div><div>We study Anderson localization of a one-dimensional quantum droplet in a speckle-like potential employing the generalized Gross–Pitaevskii equation. We compute the droplet width, density profiles, diffusion exponent and coefficient, and the localization length for both small and large droplets. Interesting classes of anomalous diffusions are obtained in transport dynamics ranging from superdiffusion to subdiffusion for a strong disorder strength. We find that above a certain critical disorder strength the droplet exhibits a transition to Anderson localization on the tails. Our results can be readily probed with recent experiments.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118138"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279151","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 : 2026-07-01Epub Date: 2026-02-27DOI: 10.1016/j.chaos.2026.118122
Vismaya V S, Sishu Shankar Muni
We investigate cyclic periodic synchronization (CPS) in a ring–star network of piecewise nonlinear discontinuous (PND) maps. While CPS has previously been reported in piecewise linear discontinuous (PLD) systems, the linear structure of such maps restricts the diversity of emergent spatiotemporal behaviours. In this work, we extend the PLD framework by introducing quadratic nonlinearities on either side of the switching manifold. Analytical expressions for border–collision bifurcation curves associated with fixed points, period–2, and higher–order periodic orbits are derived and validated through two–parameter period diagrams. When coupled in a ring–star network, the PND maps exhibit a wide spectrum of spatiotemporal patterns, including CPS, traveling waves, unsynchronized states, clustered states, and two novel collective behaviours: cluster period–2 states and cyclic periodic cluster patterns. The mechanism for CPS patterns arises from the competition and collision of synchronized clusters, which reorganize periodically to produce robust cyclic patterns. We further examine nonlocally coupled ring–star networks, demonstrating that cyclic periodic synchronization persists even under nonlocal interactions. Two-parameter regime maps in the coupling strength plane reveal how local ring coupling, global hub coupling, and coupling range collectively govern transitions among synchronized, clustered, traveling-wave, and CPS patterns. Apart from the quadratic PND map, the framework is generalized to five additional nonlinear discontinuous maps: sinusoidal, tangential, hyperbolic tangent, rational, and exponential, confirming the robustness and persistence of cyclic period-3 synchronization across diverse nonlinear formulations.
{"title":"Cyclic periodic synchronization in networks of piecewise nonlinear discontinuous maps","authors":"Vismaya V S, Sishu Shankar Muni","doi":"10.1016/j.chaos.2026.118122","DOIUrl":"10.1016/j.chaos.2026.118122","url":null,"abstract":"<div><div>We investigate cyclic periodic synchronization (CPS) in a ring–star network of piecewise nonlinear discontinuous (PND) maps. While CPS has previously been reported in piecewise linear discontinuous (PLD) systems, the linear structure of such maps restricts the diversity of emergent spatiotemporal behaviours. In this work, we extend the PLD framework by introducing quadratic nonlinearities on either side of the switching manifold. Analytical expressions for border–collision bifurcation curves associated with fixed points, period–2, and higher–order periodic orbits are derived and validated through two–parameter period diagrams. When coupled in a ring–star network, the PND maps exhibit a wide spectrum of spatiotemporal patterns, including CPS, traveling waves, unsynchronized states, clustered states, and two novel collective behaviours: cluster period–2 states and cyclic periodic cluster patterns. The mechanism for CPS patterns arises from the competition and collision of synchronized clusters, which reorganize periodically to produce robust cyclic patterns. We further examine nonlocally coupled ring–star networks, demonstrating that cyclic periodic synchronization persists even under nonlocal interactions. Two-parameter regime maps in the coupling strength plane reveal how local ring coupling, global hub coupling, and coupling range collectively govern transitions among synchronized, clustered, traveling-wave, and CPS patterns. Apart from the quadratic PND map, the framework is generalized to five additional nonlinear discontinuous maps: sinusoidal, tangential, hyperbolic tangent, rational, and exponential, confirming the robustness and persistence of cyclic period-3 synchronization across diverse nonlinear formulations.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118122"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329813","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 : 2026-07-01Epub Date: 2026-03-03DOI: 10.1016/j.chaos.2026.118075
Yuxuan Ren , Junsong Peng , Heping Zeng
The devil's staircase is a ubiquitous fractal phenomenon in nonlinear systems, and was recently extensively studied in dispersion-managed mode-locked fiber lasers with near-zero dispersion. Generally, dispersion management is realized by employing a piece of normal-dispersion gain fiber and a segment of anomalous-dispersion single-mode fiber. Thus, an amplifier similariton shaping mechanism naturally presents in the gain fiber, suggesting it is correlated to the generation of the devil's staircase. It is natural to ask whether the devil's staircase persist when the amplifier similariton shaping is absent. We address this question by numerically investigating an inverse-configuration dispersion-managed soliton laser. In this case, dispersion sign of the gain fiber and the passive fiber is reversed, thus the amplifier similariton shaping no longer exists. Interestingly, the devil's staircase is still observed in the laser. Further investigation reveals that passive similariton is correlated to the fractal dynamics. This work establishes a connection between the devil's staircase and passive similariton, providing new insights into the studies of fractal soliton dynamics and potentially inspiring novel laser designs.
{"title":"The devil's staircase and its intracavity pulse dynamics in an inverse-configuration dispersion-managed soliton laser","authors":"Yuxuan Ren , Junsong Peng , Heping Zeng","doi":"10.1016/j.chaos.2026.118075","DOIUrl":"10.1016/j.chaos.2026.118075","url":null,"abstract":"<div><div>The devil's staircase is a ubiquitous fractal phenomenon in nonlinear systems, and was recently extensively studied in dispersion-managed mode-locked fiber lasers with near-zero dispersion. Generally, dispersion management is realized by employing a piece of normal-dispersion gain fiber and a segment of anomalous-dispersion single-mode fiber. Thus, an amplifier similariton shaping mechanism naturally presents in the gain fiber, suggesting it is correlated to the generation of the devil's staircase. It is natural to ask whether the devil's staircase persist when the amplifier similariton shaping is absent. We address this question by numerically investigating an inverse-configuration dispersion-managed soliton laser. In this case, dispersion sign of the gain fiber and the passive fiber is reversed, thus the amplifier similariton shaping no longer exists. Interestingly, the devil's staircase is still observed in the laser. Further investigation reveals that passive similariton is correlated to the fractal dynamics. This work establishes a connection between the devil's staircase and passive similariton, providing new insights into the studies of fractal soliton dynamics and potentially inspiring novel laser designs.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118075"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147360616","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 : 2026-07-01Epub Date: 2026-02-17DOI: 10.1016/j.chaos.2026.118038
Zhenlong Man , JinYu Zhou , WeiQuan Wang , TianRan Dong
Medical image transmission in telemedicine environments poses significant challenges to data integrity and confidentiality, and existing security solutions generally fail to balance high-strength encryption with high-precision self-recovery. To address this integration challenge, this paper proposes a medical image security self-verification reconstruction scheme that leverages a spatiotemporal chaotic system. This approach establishes a novel dual-layer security framework. For data integrity, it combines binary block embedding with permutation ordered binary encoding to achieve precise, pixel-level localization and self-recovery of tampering within the regions of interest (ROIs) of medical images. For data confidentiality, a novel nonlinear coupled spatiotemporal chaotic system driven by deep feature fingerprints enables authorized access control for sensitive data while generating high-entropy ciphertexts, significantly enhancing the confusion and diffusion capabilities of the encryption algorithm. Experimental simulations validate the framework’s exceptional performance: the tamper detection rate reaches 93.12%, with restored images achieving an SSIM value of 0.9908. Metrics including information entropy, pixel change rate, and uniform average change intensity all approach theoretical optimal values, fully demonstrating the algorithm’s outstanding resistance to statistical and differential attacks. This research establishes a highly secure, integrated medical image transmission solution that substantially enhances the reliability of telemedicine data.
{"title":"A reconstruction scheme for secure self-verification of medical images incorporating spatiotemporal chaos encryption","authors":"Zhenlong Man , JinYu Zhou , WeiQuan Wang , TianRan Dong","doi":"10.1016/j.chaos.2026.118038","DOIUrl":"10.1016/j.chaos.2026.118038","url":null,"abstract":"<div><div>Medical image transmission in telemedicine environments poses significant challenges to data integrity and confidentiality, and existing security solutions generally fail to balance high-strength encryption with high-precision self-recovery. To address this integration challenge, this paper proposes a medical image security self-verification reconstruction scheme that leverages a spatiotemporal chaotic system. This approach establishes a novel dual-layer security framework. For data integrity, it combines binary block embedding with permutation ordered binary encoding to achieve precise, pixel-level localization and self-recovery of tampering within the regions of interest (ROIs) of medical images. For data confidentiality, a novel nonlinear coupled spatiotemporal chaotic system driven by deep feature fingerprints enables authorized access control for sensitive data while generating high-entropy ciphertexts, significantly enhancing the confusion and diffusion capabilities of the encryption algorithm. Experimental simulations validate the framework’s exceptional performance: the tamper detection rate reaches 93.12%, with restored images achieving an SSIM value of 0.9908. Metrics including information entropy, pixel change rate, and uniform average change intensity all approach theoretical optimal values, fully demonstrating the algorithm’s outstanding resistance to statistical and differential attacks. This research establishes a highly secure, integrated medical image transmission solution that substantially enhances the reliability of telemedicine data.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118038"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147386440","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 : 2026-07-01Epub Date: 2026-02-21DOI: 10.1016/j.chaos.2026.118100
Fengping Zhang, Liangqiang Zhou
This paper investigates the nonlinear dynamic behavior of shape memory alloy (SMA) oscillators subjected to combined parametric and external excitations. We employ the fast–slow decomposition method to elucidate the mechanism of relaxation oscillations, yielding an analytical expression for the quiescent interval which approximates half of the excitation period. To address global instability induced by quintic nonlinearity, we rigorously derive exact analytical expressions for homoclinic and heteroclinic orbits within a fifth-order triple-well potential and establish explicit analytical chaos thresholds using the Melnikov method. Parametric analysis indicates that increasing the damping coefficient effectively suppresses chaotic motion, whereas higher amplitudes of parametric and external excitations promote global instability. Numerical simulations corroborate the analytical predictions and further identify boundary crises as primary routes to chaos. The study reveals underlying physical mechanisms governed by the interaction between energy accumulation and rapid release. These findings provide a theoretical basis for determining stable operation boundaries and engineering design constraints for SMA smart structures.
{"title":"Bifurcations and chaos in a shape memory alloy oscillator driven by parametric and external excitations","authors":"Fengping Zhang, Liangqiang Zhou","doi":"10.1016/j.chaos.2026.118100","DOIUrl":"10.1016/j.chaos.2026.118100","url":null,"abstract":"<div><div>This paper investigates the nonlinear dynamic behavior of shape memory alloy (SMA) oscillators subjected to combined parametric and external excitations. We employ the fast–slow decomposition method to elucidate the mechanism of relaxation oscillations, yielding an analytical expression for the quiescent interval which approximates half of the excitation period. To address global instability induced by quintic nonlinearity, we rigorously derive exact analytical expressions for homoclinic and heteroclinic orbits within a fifth-order triple-well potential and establish explicit analytical chaos thresholds using the Melnikov method. Parametric analysis indicates that increasing the damping coefficient effectively suppresses chaotic motion, whereas higher amplitudes of parametric and external excitations promote global instability. Numerical simulations corroborate the analytical predictions and further identify boundary crises as primary routes to chaos. The study reveals underlying physical mechanisms governed by the interaction between energy accumulation and rapid release. These findings provide a theoretical basis for determining stable operation boundaries and engineering design constraints for SMA smart structures.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118100"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777177","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 : 2026-07-01Epub Date: 2026-02-19DOI: 10.1016/j.chaos.2026.118098
Cristian Lăzureanu , Jinyoung Cho
In this paper we investigate the occurrence of fold-Hopf bifurcations in a two-parameter family of jerk systems. Under suitable generic assumptions, we show that the system can be transformed into generic fold-Hopf jerk forms. More precisely, we consider the case where the parameters follow a saddle–node bifurcation curve and impose conditions ensuring that a pair of complex eigenvalues becomes purely imaginary. By means of Taylor expansions and smooth invertible transformations of the variables and parameters, the system is reduced to generic fold-Hopf jerk systems. We further discuss the possible types of zero-Hopf singularities arising in this setting. Using the first-order averaging theory, we establish the existence of periodic orbits bifurcating from the zero-Hopf singularity. Next, we observe that the simplest generic systems mentioned above exhibit a degenerate fold-Hopf bifurcation, and we analyze their dynamics. Finally, to illustrate the applicability of our results, we analyze the fold-Hopf bifurcation in a variant of the Rössler system expressed in an equivalent jerk form. Furthermore, we show that introducing a control term into the jerk formulation of a given system enables the corresponding original system to undergo a fold-Hopf bifurcation. In addition, we study the occurrence of the fold-Hopf bifurcation in a three-dimensional extension of the Liénard equation and we highlight the occurrence of chaotic behavior of a particular jerk system exhibiting a degenerate fold-Hopf bifurcation.
{"title":"Generic and degenerate fold-Hopf bifurcations in jerk systems: Reduction, dynamics, and applications","authors":"Cristian Lăzureanu , Jinyoung Cho","doi":"10.1016/j.chaos.2026.118098","DOIUrl":"10.1016/j.chaos.2026.118098","url":null,"abstract":"<div><div>In this paper we investigate the occurrence of fold-Hopf bifurcations in a two-parameter family of jerk systems. Under suitable generic assumptions, we show that the system can be transformed into generic fold-Hopf jerk forms. More precisely, we consider the case where the parameters follow a saddle–node bifurcation curve and impose conditions ensuring that a pair of complex eigenvalues becomes purely imaginary. By means of Taylor expansions and smooth invertible transformations of the variables and parameters, the system is reduced to generic fold-Hopf jerk systems. We further discuss the possible types of zero-Hopf singularities arising in this setting. Using the first-order averaging theory, we establish the existence of periodic orbits bifurcating from the zero-Hopf singularity. Next, we observe that the simplest generic systems mentioned above exhibit a degenerate fold-Hopf bifurcation, and we analyze their dynamics. Finally, to illustrate the applicability of our results, we analyze the fold-Hopf bifurcation in a variant of the Rössler system expressed in an equivalent jerk form. Furthermore, we show that introducing a control term into the jerk formulation of a given system enables the corresponding original system to undergo a fold-Hopf bifurcation. In addition, we study the occurrence of the fold-Hopf bifurcation in a three-dimensional extension of the Liénard equation and we highlight the occurrence of chaotic behavior of a particular jerk system exhibiting a degenerate fold-Hopf bifurcation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118098"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777188","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 : 2026-07-01Epub Date: 2026-02-18DOI: 10.1016/j.chaos.2026.118060
Jia-Bao Liu , Meng-Yuan Yu , Guo-Jun Cai , Jinde Cao
In this paper, the leader–follower coherence and spectral properties of weighted recursive networks are investigated. Firstly, the analytical solution for leader–follower coherence dynamics is derived, which provides a rigorous theoretical foundation for performance analysis. Secondly, the influence of network structural parameters on coherence behavior is systematically examined. Thirdly, the collaborative capability of the network is characterized by the Kirchhoff index and the global mean first-pass time (GMFPT). These findings unveil the intrinsic coupling between topological design and dynamical performance in weighted recursive networks, which provides theoretical guidance for constructing robust and scalable multi-agent systems.
{"title":"The leader–follower coherence and spectral properties of weighted recursive networks under noise disturbance","authors":"Jia-Bao Liu , Meng-Yuan Yu , Guo-Jun Cai , Jinde Cao","doi":"10.1016/j.chaos.2026.118060","DOIUrl":"10.1016/j.chaos.2026.118060","url":null,"abstract":"<div><div>In this paper, the leader–follower coherence and spectral properties of weighted recursive networks are investigated. Firstly, the analytical solution for leader–follower coherence dynamics is derived, which provides a rigorous theoretical foundation for performance analysis. Secondly, the influence of network structural parameters on coherence behavior is systematically examined. Thirdly, the collaborative capability of the network is characterized by the Kirchhoff index and the global mean first-pass time (GMFPT). These findings unveil the intrinsic coupling between topological design and dynamical performance in weighted recursive networks, which provides theoretical guidance for constructing robust and scalable multi-agent systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118060"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146777677","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 : 2026-07-01Epub Date: 2026-02-25DOI: 10.1016/j.chaos.2026.118150
Mingli Lei , Jazmín-Susana De la Cruz-García , Juan Bory-Reyes , Aldo Ramirez-Arellano
Extropy is a complementary measure to entropy, proposed as its informational dual. While entropy quantifies the uncertainty or disorder of a distribution, extropy quantifies the certainty or order of the distribution. Extropy has been used in information theory, statistical modeling, complex networks, adaptive systems, and decision-making under uncertainty. From this perspective, the dual information dimension is introduced. The dual information dimension provides an alternative way to measure certainty and network organization by exploiting extropy, offering a complementary view to entropy-based information dimensions.
In the present study, we propose a reformulation of the asymptotes for the dual information dimension, denoted by , using the nonlinear Logistic4P (four-parameter logistic), Gompertz, Richards (4 and 5 parameters), and von Bertalanffy mathematical models. To validate the proposed reformulation, a representative set of 16 real-world networks, covering different areas of knowledge and practical applications, was used. The results indicate that the optimal nonlinear model depends on the dual used. Indeed, Richards4 and Richards5 excel in the Shannon and Tsallis , respectively, while Logistic4P and Gompertz offer better fits in the Fractional and Rényi . However, no single model emerges as optimal across all cases, highlighting the need to select a model based on the specific characteristics of each network and the informational approach employed.
{"title":"Nonlinear asymptotes of dual information dimension of complex networks","authors":"Mingli Lei , Jazmín-Susana De la Cruz-García , Juan Bory-Reyes , Aldo Ramirez-Arellano","doi":"10.1016/j.chaos.2026.118150","DOIUrl":"10.1016/j.chaos.2026.118150","url":null,"abstract":"<div><div>Extropy is a complementary measure to entropy, proposed as its informational dual. While entropy quantifies the uncertainty or disorder of a distribution, extropy quantifies the certainty or order of the distribution. Extropy has been used in information theory, statistical modeling, complex networks, adaptive systems, and decision-making under uncertainty. From this perspective, the dual information dimension is introduced. The dual information dimension provides an alternative way to measure certainty and network organization by exploiting extropy, offering a complementary view to entropy-based information dimensions.</div><div>In the present study, we propose a reformulation of the asymptotes for the dual information dimension, denoted by <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi><mi>d</mi></mrow></msub></math></span>, using the nonlinear Logistic4P (four-parameter logistic), Gompertz, Richards (4 and 5 parameters), and von Bertalanffy mathematical models. To validate the proposed reformulation, a representative set of 16 real-world networks, covering different areas of knowledge and practical applications, was used. The results indicate that the optimal nonlinear model depends on the dual <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi><mi>d</mi></mrow></msub></math></span> used. Indeed, Richards4 and Richards5 excel in the Shannon and Tsallis <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi><mi>d</mi></mrow></msub></math></span>, respectively, while Logistic4P and Gompertz offer better fits in the Fractional <span><math><mrow><mo>(</mo><mi>q</mi><mo>,</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow></math></span> and Rényi <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>i</mi><mi>d</mi></mrow></msub></math></span>. However, no single model emerges as optimal across all cases, highlighting the need to select a model based on the specific characteristics of each network and the informational approach employed.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118150"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147279121","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 : 2026-07-01Epub Date: 2026-02-27DOI: 10.1016/j.chaos.2026.118163
Jie Yang , Jing Peng , Yasir Ramzan , Sanyi Tang , Jie Lou
Dengue fever is a mosquito-borne infectious disease that poses a significant threat to public health and safety. It is crucial to establish the most appropriate mathematical model and estimate the most reliable parameters to simulate the epidemic and quantify control measures. Therefore, an ODE model, a FDE model and a discrete model are constructed. Three parameter estimation methods (PINNs/fPINNs/Euler-PINNs) are applied to three models (ODE/FDE/discrete), respectively, with data in Singapore. Specifically, a variable-dependent weight optimization strategy (VDWOS) for the inverse problem is newly proposed in this paper, which is compared with the traditional weight optimization strategy (TWOS). For theoretical analysis, there are essential differences: when the endemic equilibrium of the ODE/FDE model is globally asymptotically stable, the discrete model may exhibit a flip bifurcation, resulting in a disruption of stability. For numerical simulation, by comparing TWOS and VDWOS for three models, VDWOS yields more reliable parameters and time-varying parameter without specific function assumptions. Furthermore, an LSTM network is applied to predict obtained by VDWOS, and the prediction solution is highly consistent with the test data. Meanwhile, through sensitivity analysis, the model-based numerical reconstruction solution exhibits significant responsiveness, which neural networks cannot achieve. However, the ODE model and the discrete model exhibit a high degree of consistency in their specific numerical conclusions, while the FDE model yields significantly different results. This study provides valuable insights into the crucial issue of model selection in the fields of infectious disease prediction and early warning, pest control, and tumor treatment.
{"title":"A systematic comparative analysis of modeling methods and variable-dependent weight optimization strategy for PINNs","authors":"Jie Yang , Jing Peng , Yasir Ramzan , Sanyi Tang , Jie Lou","doi":"10.1016/j.chaos.2026.118163","DOIUrl":"10.1016/j.chaos.2026.118163","url":null,"abstract":"<div><div>Dengue fever is a mosquito-borne infectious disease that poses a significant threat to public health and safety. It is crucial to establish the most appropriate mathematical model and estimate the most reliable parameters to simulate the epidemic and quantify control measures. Therefore, an ODE model, a FDE model and a discrete model are constructed. Three parameter estimation methods (PINNs/fPINNs/Euler-PINNs) are applied to three models (ODE/FDE/discrete), respectively, with data in Singapore. Specifically, a variable-dependent weight optimization strategy (VDWOS) for the inverse problem is newly proposed in this paper, which is compared with the traditional weight optimization strategy (TWOS). For theoretical analysis, there are essential differences: when the endemic equilibrium of the ODE/FDE model is globally asymptotically stable, the discrete model may exhibit a flip bifurcation, resulting in a disruption of stability. For numerical simulation, by comparing TWOS and VDWOS for three models, VDWOS yields more reliable parameters and time-varying parameter <span><math><mrow><mi>β</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> without specific function assumptions. Furthermore, an LSTM network is applied to predict <span><math><mrow><mi>β</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> obtained by VDWOS, and the prediction solution is highly consistent with the test data. Meanwhile, through sensitivity analysis, the model-based numerical reconstruction solution exhibits significant responsiveness, which neural networks cannot achieve. However, the ODE model and the discrete model exhibit a high degree of consistency in their specific numerical conclusions, while the FDE model yields significantly different results. This study provides valuable insights into the crucial issue of model selection in the fields of infectious disease prediction and early warning, pest control, and tumor treatment.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"208 ","pages":"Article 118163"},"PeriodicalIF":5.6,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147329809","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 : 2026-07-01Epub Date: 2026-02-26DOI: 10.1016/j.chaos.2026.118152
Shuaiyang Jiao , Liyuan Xue , Yubo Li , Juntong Wu , Aizeng Li
This study investigates the impact of the taillight effect on the stability of mixed traffic flow. Constrained by physiological limitations, human drivers inevitably exhibit visual reaction delays when perceiving brake lights. Conversely, connected vehicles leverage V2X communication to receive electronic signals, enabling instantaneous feedback and beyond-visual-range perception. These distinct characteristics create a competitive relationship regarding their contributions to system stability. Thus, this study explicitly defines this competition by employing the connected vehicle penetration rate as a weighting parameter. By incorporating this into a lattice hydrodynamic model, we quantify the unique competitive mechanism between the lag of human visual perception and the instantaneity of V2X communication. Through linear stability analysis, we derive the critical stability criterion and reveal how the penetration rate of connected vehicles offsets the instability caused by human physiological delay. On this basis, we carry out nonlinear analysis using the reductive perturbation method to derive the modified mKdV equation near the critical point and obtain the analytical solution for the kink-antikink soliton. Numerical simulations confirm the theoretical predictions and demonstrate that increasing the penetration rate of connected vehicles significantly modifies the dispersion coefficient of traffic flow. These results substantiate that the competition mechanism under the taillight effect effectively eliminates the hysteresis loop and phantom jam caused by visual delay and enhances the robustness of the traffic system against the physiological limitations of human drivers.
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