Pub Date : 2025-12-13DOI: 10.1016/j.physd.2025.135055
Chris Budd , Rachel Kuske
We study critical relationships between the smoothness parameter for the underlying fold bifurcation and the noise level in the context of B-tipping near smooth and non-smooth dynamic fold bifurcations. The motivation is the Stommel 2-box model, a piecewise-smooth continuous dynamical system modeling thermohaline circulation in the North Atlantic, and related climate models. These contain non-smooth fold bifurcations which arise when a saddle-point and a stable focus meet at a border collision bifurcation. An asymptotic analysis of the corresponding Fokker-Planck Equation (FPE) for the stochastic system provides insight into critical noise levels, depending on the relative rate of parameter variation and a measure of smoothness of the underlying bifurcation. Critical scales are obtained from different reductions of the FPE, identifying cases where noise may advance tipping relative to deterministic behavior. Applying this approach for B-tipping near both smooth and non-smooth folds shows that the non-smooth case has greater sensitivity to smaller noise levels, with a smaller critical scale for noise-advanced tipping in the non-smooth case. Since these results do not depend on obtaining a solution of the FPE, the approach can be adapted to multi-degree-of-freedom models and in other applications.
{"title":"Critical noise for advanced dynamic B-tipping in nearly non-smooth Stommel-type models","authors":"Chris Budd , Rachel Kuske","doi":"10.1016/j.physd.2025.135055","DOIUrl":"10.1016/j.physd.2025.135055","url":null,"abstract":"<div><div>We study critical relationships between the smoothness parameter for the underlying fold bifurcation and the noise level in the context of B-tipping near smooth and non-smooth dynamic fold bifurcations. The motivation is the Stommel 2-box model, a piecewise-smooth continuous dynamical system modeling thermohaline circulation in the North Atlantic, and related climate models. These contain non-smooth fold bifurcations which arise when a saddle-point and a stable focus meet at a border collision bifurcation. An asymptotic analysis of the corresponding Fokker-Planck Equation (FPE) for the stochastic system provides insight into critical noise levels, depending on the relative rate of parameter variation and a measure of smoothness of the underlying bifurcation. Critical scales are obtained from different reductions of the FPE, identifying cases where noise may advance tipping relative to deterministic behavior. Applying this approach for B-tipping near both smooth and non-smooth folds shows that the non-smooth case has greater sensitivity to smaller noise levels, with a smaller critical scale for noise-advanced tipping in the non-smooth case. Since these results do not depend on obtaining a solution of the FPE, the approach can be adapted to multi-degree-of-freedom models and in other applications.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"488 ","pages":"Article 135055"},"PeriodicalIF":2.9,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-13DOI: 10.1016/j.physd.2025.135081
Yi Ding , Chun Yan , Wei Liu , Jiahui Liu
Risk contagion in financial systems presents spatially hierarchical patterns and temporally nonlinear accumulation. To explore this dynamic contagion process, this paper constructs a multilayer dynamic financial network incorporating three types of interbank interactions: interbank lending, cross-holding, and overlapping investment portfolios. We extend the classical Eisenberg-NOE clearing model to a multiplex and sequential dynamic setting, characterizing the propagation of risk through nonlinear clearing dynamics. Bank defaults are classified into illiquidity and insolvency, with temporal evolution achieved through deferred debt. Next, we model the government control as a Markov decision process and introduce fairness constraints to balance systemic stability and equity. Finally, we use Monte Carlo simulations to analyze the numerical results obtained with different control strategies and provide robustness tests.
{"title":"Sequential clearing dynamics and systemic risk control for multilayer financial system","authors":"Yi Ding , Chun Yan , Wei Liu , Jiahui Liu","doi":"10.1016/j.physd.2025.135081","DOIUrl":"10.1016/j.physd.2025.135081","url":null,"abstract":"<div><div>Risk contagion in financial systems presents spatially hierarchical patterns and temporally nonlinear accumulation. To explore this dynamic contagion process, this paper constructs a multilayer dynamic financial network incorporating three types of interbank interactions: interbank lending, cross-holding, and overlapping investment portfolios. We extend the classical Eisenberg-NOE clearing model to a multiplex and sequential dynamic setting, characterizing the propagation of risk through nonlinear clearing dynamics. Bank defaults are classified into illiquidity and insolvency, with temporal evolution achieved through deferred debt. Next, we model the government control as a Markov decision process and introduce fairness constraints to balance systemic stability and equity. Finally, we use Monte Carlo simulations to analyze the numerical results obtained with different control strategies and provide robustness tests.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135081"},"PeriodicalIF":2.9,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Switching power conversion circuits are of great importance within a wide variety of applications, including automotive, wearable device, and so on. Their widespread use is largely due to their high efficiency and small size. However, when such circuits are subject to capacitor degradation, undesired turbulence and a degradation in the overall performance of the converter circuit can be observed. This paper investigates the effect of capacitor degradation on the occurrence of chattering in high-side gate driver circuits within power conversion systems. We introduce a simple mathematical model of a high-side gate driver circuit, which incorporates a hysteresis characteristic as a result of the under-voltage lockout (UVLO) function. We analytically derived the conditions in which chattering events occur and how the number of switching events changes. These analytical expressions were achieved by analyzing the period of the return map and identifying the thresholds that can be used to characterize the different behaviors that the system exhibits. In this work, we obtain a relationship between capacitor degradation and the chattering events.
{"title":"Chattering phenomenon in high-side gate driver circuits with degraded capacitors","authors":"Daisuke Ito , Yusuke Goto , Kaito Kato , Hiroyuki Asahara , Takuji Kousaka","doi":"10.1016/j.physd.2025.135076","DOIUrl":"10.1016/j.physd.2025.135076","url":null,"abstract":"<div><div>Switching power conversion circuits are of great importance within a wide variety of applications, including automotive, wearable device, and so on. Their widespread use is largely due to their high efficiency and small size. However, when such circuits are subject to capacitor degradation, undesired turbulence and a degradation in the overall performance of the converter circuit can be observed. This paper investigates the effect of capacitor degradation on the occurrence of chattering in high-side gate driver circuits within power conversion systems. We introduce a simple mathematical model of a high-side gate driver circuit, which incorporates a hysteresis characteristic as a result of the under-voltage lockout (UVLO) function. We analytically derived the conditions in which chattering events occur and how the number of switching events changes. These analytical expressions were achieved by analyzing the period of the return map and identifying the thresholds that can be used to characterize the different behaviors that the system exhibits. In this work, we obtain a relationship between capacitor degradation and the chattering events.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135076"},"PeriodicalIF":2.9,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-12DOI: 10.1016/j.physd.2025.135074
Uday Chand De , Füsun ÖZEN ZENGİN , Sezgin ALTAY DEMIRBAG , Krishnendu De
In the present paper, we investigate the classification of a spacetime admitting gradient Ricci-Yamabe solitons in special conditions. We acquire that such a spacetime obeying divergence-free Weyl tensor becomes a generalized Robertson-Walker spacetime as well as a static spacetime and the spacetime represents dark matter era. Also, we show that such a spacetime is a Robertson-Walker spacetime and it is of Petrov type “O”. Moreover, it has also been investigated under what conditions this spacetime turns into a stiff matter era. In the last section of this paper, we examine the effect of this spacetime under f(R)-gravity scenario and derive several energy conditions graphically using two different models.
{"title":"Characterizations of a spacetime admitting gradient Ricci-Yamabe solitons and f(R)-gravity","authors":"Uday Chand De , Füsun ÖZEN ZENGİN , Sezgin ALTAY DEMIRBAG , Krishnendu De","doi":"10.1016/j.physd.2025.135074","DOIUrl":"10.1016/j.physd.2025.135074","url":null,"abstract":"<div><div>In the present paper, we investigate the classification of a spacetime admitting gradient Ricci-Yamabe solitons in special conditions. We acquire that such a spacetime obeying divergence-free Weyl tensor becomes a generalized Robertson-Walker spacetime as well as a static spacetime and the spacetime represents dark matter era. Also, we show that such a spacetime is a Robertson-Walker spacetime and it is of Petrov type “O”. Moreover, it has also been investigated under what conditions this spacetime turns into a stiff matter era. In the last section of this paper, we examine the effect of this spacetime under <em>f</em>(<em>R</em>)-gravity scenario and derive several energy conditions graphically using two different models.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135074"},"PeriodicalIF":2.9,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-12DOI: 10.1016/j.physd.2025.135080
Pedro Gatón-Pérez , Enrique Rodríguez-Fernández , Rodolfo Cuerno
The occurrence of strong coupling or nonlinear scaling behavior for kinetically rough interfaces whose dynamics are conserved, but not necessarily variational, remains to be fully understood. Here we formulate and study a family of conserved stochastic evolution equations for one-dimensional interfaces, whose nonlinearity depends on a parameter n, thus generalizing that of the stochastic Burgers equation, whose behavior is retrieved for . This family of equations includes as particular instances a stochastic porous medium equation and other continuum models relevant to various hard and soft condensed matter systems. We perform a one-loop dynamical renormalization group analysis of the equations, which contemplates strong coupling scaling exponents that depend on the value of n and may or may not imply vertex renormalization. These analytical expectations are contrasted with explicit numerical simulations of the equations with and 3. For odd n, numerical stability issues have required us to generalize the scheme originally proposed for by T. Sasamoto and H. Spohn [J. Stat. Phys. 137, 917 (2009)]. Precisely for and 3, and at variance with the and 2 cases (whose numerical exponents are consistent with non-renormalization of the vertex), numerical strong coupling exponent values are obtained which suggest vertex renormalization, akin to that reported for the celebrated conserved Kardar-Parisi-Zhang (cKPZ) equation. We also study numerically the statistics of height fluctuations, whose probability distribution function turns out (at variance with cKPZ) to have zero skewness for long times and at saturation, irrespective of the value of n. However, the kurtosis is non-Gaussian, further supporting the conclusion on strong coupling asymptotic behavior. The zero skewness seems related with space symmetries of the and 2 equations, and with an emergent symmetry at the strong coupling fixed point for odd values of n.
对于动力学守恒但不一定变分的动力学粗糙界面，其强耦合或非线性标度行为的发生仍有待充分理解。本文建立并研究了一类非线性依赖于参数n的一维界面的守恒随机演化方程，从而推广了n=0时可获取其行为的随机Burgers方程。这一系列方程包括随机多孔介质方程和其他与各种硬、软凝聚态系统相关的连续介质模型。我们对方程进行了一个单环动态重整化群分析，该分析考虑了依赖于n值的强耦合缩放指数，并且可能或可能不意味着顶点重整化。这些分析期望与n= 1,2,3的方程的显式数值模拟进行了对比。对于奇数n，数值稳定性问题要求我们推广最初由T. Sasamoto和H. Spohn在n=0时提出的方案[J]。[j].物理学报，2003,17(5)。精确地说，对于n=1和3，并与n=0和2的情况（其数值指数与顶点的非重整化一致）不同，得到了数值强耦合指数值，表明顶点重整化，类似于著名的保守kardar - paris - zhang （cKPZ）方程的报告。我们还研究了高度波动的数值统计，其概率分布函数（与cKPZ不同）在长时间和饱和时，无论n的值如何，都具有零偏度。然而，峰度是非高斯的，进一步支持了强耦合渐近行为的结论。零偏度似乎与n=0和n= 2方程的空间对称性有关，并且与奇数n值的强耦合不动点的突现对称性有关。
{"title":"Universality classes with strong coupling in conserved surface roughening: explicit vs emergent symmetries","authors":"Pedro Gatón-Pérez , Enrique Rodríguez-Fernández , Rodolfo Cuerno","doi":"10.1016/j.physd.2025.135080","DOIUrl":"10.1016/j.physd.2025.135080","url":null,"abstract":"<div><div>The occurrence of strong coupling or nonlinear scaling behavior for kinetically rough interfaces whose dynamics are conserved, but not necessarily variational, remains to be fully understood. Here we formulate and study a family of conserved stochastic evolution equations for one-dimensional interfaces, whose nonlinearity depends on a parameter <em>n</em>, thus generalizing that of the stochastic Burgers equation, whose behavior is retrieved for <span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></math></span>. This family of equations includes as particular instances a stochastic porous medium equation and other continuum models relevant to various hard and soft condensed matter systems. We perform a one-loop dynamical renormalization group analysis of the equations, which contemplates strong coupling scaling exponents that depend on the value of <em>n</em> and may or may not imply vertex renormalization. These analytical expectations are contrasted with explicit numerical simulations of the equations with <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo></mrow></math></span> and 3. For odd <em>n</em>, numerical stability issues have required us to generalize the scheme originally proposed for <span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></math></span> by T. Sasamoto and H. Spohn [J. Stat. Phys. <strong>137</strong>, 917 (2009)]. Precisely for <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span> and 3, and at variance with the <span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></math></span> and 2 cases (whose numerical exponents are consistent with non-renormalization of the vertex), numerical strong coupling exponent values are obtained which suggest vertex renormalization, akin to that reported for the celebrated conserved Kardar-Parisi-Zhang (cKPZ) equation. We also study numerically the statistics of height fluctuations, whose probability distribution function turns out (at variance with cKPZ) to have zero skewness for long times and at saturation, irrespective of the value of <em>n</em>. However, the kurtosis is non-Gaussian, further supporting the conclusion on strong coupling asymptotic behavior. The zero skewness seems related with space symmetries of the <span><math><mrow><mi>n</mi><mo>=</mo><mn>0</mn></mrow></math></span> and 2 equations, and with an emergent symmetry at the strong coupling fixed point for odd values of <em>n</em>.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135080"},"PeriodicalIF":2.9,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-11DOI: 10.1016/j.physd.2025.135075
Mustafa Turkyilmazoglu , Abdulaziz Alotaibi
This study investigates the unsteady stagnation-point flow around a permeable flat body, where the body’s motion relative to the impinging flow can vary with time. Additionally, the surface is subjected to a time-varying magnetic field. We first transform the governing equations of unsteady motion into a similarity form using specific forms of time-dependent variables. This allows us to explore potential exact solutions, leading to the identification of special exponential solutions applicable to both front and rear stagnation-point flows. To further comprehend the interplay of magnetic field, wall transpiration, and wall movement on the stagnation-point flow development, we conduct comprehensive numerical simulations. These simulations clarify the boundaries of unique and multiple solution regimes influenced by these physical parameters. Furthermore, we identify distinct regimes of separated and attached stagnant flow, which hold significant relevance in flow control applications in fluid mechanics and industrial engineering fields. Wall suction acts to regularize the upper branch solutions, and magnetic field enhances the domain of dual solutions, with further enlarging the separated flow zone for the front stagnation-point flow. However, for the rear stagnation-point flow, the upper and lower branches of solutions are linked by the magnetic field.
{"title":"MHD Front and rear stagnation-point flow of a moving permeable flat surface","authors":"Mustafa Turkyilmazoglu , Abdulaziz Alotaibi","doi":"10.1016/j.physd.2025.135075","DOIUrl":"10.1016/j.physd.2025.135075","url":null,"abstract":"<div><div>This study investigates the unsteady stagnation-point flow around a permeable flat body, where the body’s motion relative to the impinging flow can vary with time. Additionally, the surface is subjected to a time-varying magnetic field. We first transform the governing equations of unsteady motion into a similarity form using specific forms of time-dependent variables. This allows us to explore potential exact solutions, leading to the identification of special exponential solutions applicable to both front and rear stagnation-point flows. To further comprehend the interplay of magnetic field, wall transpiration, and wall movement on the stagnation-point flow development, we conduct comprehensive numerical simulations. These simulations clarify the boundaries of unique and multiple solution regimes influenced by these physical parameters. Furthermore, we identify distinct regimes of separated and attached stagnant flow, which hold significant relevance in flow control applications in fluid mechanics and industrial engineering fields. Wall suction acts to regularize the upper branch solutions, and magnetic field enhances the domain of dual solutions, with further enlarging the separated flow zone for the front stagnation-point flow. However, for the rear stagnation-point flow, the upper and lower branches of solutions are linked by the magnetic field.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135075"},"PeriodicalIF":2.9,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-09DOI: 10.1016/j.physd.2025.135077
Ulrich Simo Domguia , Vinod V , Bipin Balaram , Paul Woafo
In this work, we consider the Grudzinski-Zebrowski oscillator excited periodically and analyze its dynamical behaviors with reference to the effects of external stimuli on electric node of the heart. Mathematical analysis, numerical and microcontroller simulations are employed. The nonlinear differential equation of the GZ oscillator is solved both analytically and numerically using averaging and the four-order Runge-Kutta methods. The results obtained are shown in terms of asymptotic solution, bifurcation diagrams, corresponding Lyapunov exponents variation and time histories. The bifurcation diagrams reveal the presence of winding number, chaos, bursting, spiking and pulse oscillations. The analytical calculations match well with the numerical results. These behaviors are exhibited experimentally using microcontroller simulations with a good qualitative agreement.
{"title":"Characterization of the dynamics of free and excited Grudzinski-Zebrowski (GZ) oscillator using mathematical methods and microcontroller simulation experiment","authors":"Ulrich Simo Domguia , Vinod V , Bipin Balaram , Paul Woafo","doi":"10.1016/j.physd.2025.135077","DOIUrl":"10.1016/j.physd.2025.135077","url":null,"abstract":"<div><div>In this work, we consider the Grudzinski-Zebrowski oscillator excited periodically and analyze its dynamical behaviors with reference to the effects of external stimuli on electric node of the heart. Mathematical analysis, numerical and microcontroller simulations are employed. The nonlinear differential equation of the GZ oscillator is solved both analytically and numerically using averaging and the four-order Runge-Kutta methods. The results obtained are shown in terms of asymptotic solution, bifurcation diagrams, corresponding Lyapunov exponents variation and time histories. The bifurcation diagrams reveal the presence of winding number, chaos, bursting, spiking and pulse oscillations. The analytical calculations match well with the numerical results. These behaviors are exhibited experimentally using microcontroller simulations with a good qualitative agreement.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"487 ","pages":"Article 135077"},"PeriodicalIF":2.9,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145766053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-09DOI: 10.1016/j.physd.2025.135078
Jialong Wang, Shaohui Yan, Jiandong Zhang
This parper introduces an innovative discrete local active memristor and demonstrates its local active characteristics using DC V-I curves. The proposed memristor simulates the function of biological synapses, and further constructs a discrete coupled Hindmarsh-Rose and FitzHugh-Nagumo (HR-FHN) neuron model. It calculates and analyzes its fixed points and Hamiltonian energy, clarifying the energy dynamics and equilibrium point mechanism of firing model conversion in this system. At the same time, theoretical analysis and numerical simulation show that it can generate multiple firing models under the influence of local active memristors. In addition, complex chaotic behaviors are observed, such as the coexistence of different firing models, transient chaos, and offset boosting. It is implemented as a digital circuit using Field-Programmable Gate Array (FPGA), demonstrating the dynamic control and physical reliability of the discrete local active memristive neuron model.
{"title":"Discrete Local Active Memristive HR and FHN Coupled Neuron Model and FPGA Implementation","authors":"Jialong Wang, Shaohui Yan, Jiandong Zhang","doi":"10.1016/j.physd.2025.135078","DOIUrl":"10.1016/j.physd.2025.135078","url":null,"abstract":"<div><div>This parper introduces an innovative discrete local active memristor and demonstrates its local active characteristics using DC <em>V-I</em> curves. The proposed memristor simulates the function of biological synapses, and further constructs a discrete coupled Hindmarsh-Rose and FitzHugh-Nagumo (HR-FHN) neuron model. It calculates and analyzes its fixed points and Hamiltonian energy, clarifying the energy dynamics and equilibrium point mechanism of firing model conversion in this system. At the same time, theoretical analysis and numerical simulation show that it can generate multiple firing models under the influence of local active memristors. In addition, complex chaotic behaviors are observed, such as the coexistence of different firing models, transient chaos, and offset boosting. It is implemented as a digital circuit using Field-Programmable Gate Array (FPGA), demonstrating the dynamic control and physical reliability of the discrete local active memristive neuron model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135078"},"PeriodicalIF":2.9,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Precise timing in neuronal spiking is important for effective signal processing and transmission in excitable systems. Disruptions to the timing accuracy of neuronal synchronization can impair brain function and contribute to neurodegenerative diseases such as Huntington’s disease. In this work, we employ a technique called “dynamic entrainment” to determine the optimal time gap between successive input pulses required to bring and maintain the system in a 1:1 entrainment regime. Unlike the previous study that applied dynamic entrainment to the four-dimensional Hodgkin-Huxley model, we adopt the approach for the two-dimensional Morris-Lecar model. The reduced dimensionality of Morris-Lecar makes it computationally efficient while still capturing essential features of excitability. It also facilitates straightforward phase plane analysis providing geometric insights into the success of dynamic entrainment. It demonstrates that dynamic entrainment allows achieving and sustaining 1:1 entrainment when fixed periodic forcing fails. We also explore the use of dynamic entrainment at higher-order resonances within the Arnold tongue. By dynamically changing the inter-pulse interval, we achieved 1:1 entrainment, and the effective period of the selected point shifted to an originally 1:1 region.
{"title":"Dynamic entrainment of neuronal spiking: A phase plane analysis and a data-driven approach","authors":"Lawan Wijayasooriya , Soheil Saghafi , Emel Khan , Pejman Sanaei","doi":"10.1016/j.physd.2025.135071","DOIUrl":"10.1016/j.physd.2025.135071","url":null,"abstract":"<div><div>Precise timing in neuronal spiking is important for effective signal processing and transmission in excitable systems. Disruptions to the timing accuracy of neuronal synchronization can impair brain function and contribute to neurodegenerative diseases such as Huntington’s disease. In this work, we employ a technique called “dynamic entrainment” to determine the optimal time gap between successive input pulses required to bring and maintain the system in a 1:1 entrainment regime. Unlike the previous study that applied dynamic entrainment to the four-dimensional Hodgkin-Huxley model, we adopt the approach for the two-dimensional Morris-Lecar model. The reduced dimensionality of Morris-Lecar makes it computationally efficient while still capturing essential features of excitability. It also facilitates straightforward phase plane analysis providing geometric insights into the success of dynamic entrainment. It demonstrates that dynamic entrainment allows achieving and sustaining 1:1 entrainment when fixed periodic forcing fails. We also explore the use of dynamic entrainment at higher-order resonances within the Arnold tongue. By dynamically changing the inter-pulse interval, we achieved 1:1 entrainment, and the effective period of the selected point shifted to an originally 1:1 region.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"486 ","pages":"Article 135071"},"PeriodicalIF":2.9,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145840769","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-08DOI: 10.1016/j.physd.2025.135072
Ozgur Afsar , Sevda Saltik , Fatimat Bughluyeva
Spatially ordered patterns that may emerge in various natural phenomena as the result of an evolution cause an increasing order within the system until forming a stationary state. One of special types of such patterns, highly complex cantor sets, arises as a result of successive bifurcations of trajectories of a dynamical system throughout its evolution in the control parameter space. It is well known that evolution towards such ordered structures requires a decrease in the entropy of the system, which can lead to an increase in the degree of complexity of the phase space. Although there are many entropy-based complexity measures in the literature, exploring the appropriate entropy that is capable of explaining such an evolution process and defining the degree of complexity of the structure of the physical system is one of the main research topics in complexity science. We evaluated possible total energy values of Frenkel-Kontorova-type independent chains with a free boundary condition at static equilibrium. We show that the ensemble of the total energies represents period doublings and chaotic band-mergings if one changes the control parameter, which is the value of the amplitude of the substrate potential. The periods of the total energies accumulate at a critical value, causing the emergence of self-similar and spatially organized fractal patterns. Using the energy distributions in the control parameter space, we also calculate entropy-based complexity measures: Shannon, Kullback-Leibler and q-Renormalized entropies. We show that the q-renormalized entropy behaves according to the well-known low-entropy criteria of self-organization, whereas the Shannon and Kullback-Leibler entropies cannot. This implies that the q-renormalized entropy is an appropriate entropy to explore the emergence and disappearance of spatially organized fractal energy patterns and to evaluate their complexities.
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