Pub Date : 2025-11-12DOI: 10.1016/j.physd.2025.135028
Daniel Pérez-Palau , Diego Enrique Pico-Lache
Lyapunov exponents have been utilized extensively in the detection of chaos and stability. Various alternatives, such as finite-time Lyapunov exponents and Lagrangian descriptors, have been recently proposed with the objective of reducing the computational demands of the former. In this study, we introduce a novel indicator inspired by the Lagrangian descriptors for discrete systems. This approach facilitates the exploration and detection of chaos in pendular systems through the discretization of the system using Poincaré sections. A comparison of the results obtained with those from the literature was conducted, yielding successful outcomes. A drawback of those indicators is its high computational burden. An optimization procedure has been successfully implemented. This algorithm reduces the computational time by a factor up to 20 for some indicators. This new procedure outputs favourable results for those indicators that explore large system times.
{"title":"Optimization of dynamics indicators in pendular systems","authors":"Daniel Pérez-Palau , Diego Enrique Pico-Lache","doi":"10.1016/j.physd.2025.135028","DOIUrl":"10.1016/j.physd.2025.135028","url":null,"abstract":"<div><div>Lyapunov exponents have been utilized extensively in the detection of chaos and stability. Various alternatives, such as finite-time Lyapunov exponents and Lagrangian descriptors, have been recently proposed with the objective of reducing the computational demands of the former. In this study, we introduce a novel indicator inspired by the Lagrangian descriptors for discrete systems. This approach facilitates the exploration and detection of chaos in pendular systems through the discretization of the system using Poincaré sections. A comparison of the results obtained with those from the literature was conducted, yielding successful outcomes. A drawback of those indicators is its high computational burden. An optimization procedure has been successfully implemented. This algorithm reduces the computational time by a factor up to 20 for some indicators. This new procedure outputs favourable results for those indicators that explore large system times.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135028"},"PeriodicalIF":2.9,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527024","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 : 2025-11-11DOI: 10.1016/j.physd.2025.135034
Dev Jasuja , P.J. Atzberger
We introduce exponential numerical integration methods for handling stiff stochastic dynamical systems having time-varying dissipative operators and fluctuations. Time-dependence presents challenges for exponentiation to obtain tractable expressions for evaluation, especially when the dissipative operators do not commute in time. We introduce approaches based on statistical mechanics and Magnus expansions to obtain stochastic integration methods that exhibit fluctuation–dissipation balance and other properties that facilitate computations. We show how practical computational methods can be developed to approximate and evaluate the contributions of the resulting stochastic expressions. We demonstrate our methods on several examples, including time-varying SDEs that arise in particle simulations and for SPDEs that model fluctuations in concentration fields of spatially-extended systems. Our introduced approaches provide methods for preserving statistical structures and other properties to obtain exponential numerical integrators for handling stiffness in time-varying stochastic dynamical systems.
{"title":"Magnus exponential integrators for stiff time-varying stochastic systems","authors":"Dev Jasuja , P.J. Atzberger","doi":"10.1016/j.physd.2025.135034","DOIUrl":"10.1016/j.physd.2025.135034","url":null,"abstract":"<div><div>We introduce exponential numerical integration methods for handling stiff stochastic dynamical systems having time-varying dissipative operators and fluctuations. Time-dependence presents challenges for exponentiation to obtain tractable expressions for evaluation, especially when the dissipative operators do not commute in time. We introduce approaches based on statistical mechanics and Magnus expansions to obtain stochastic integration methods that exhibit fluctuation–dissipation balance and other properties that facilitate computations. We show how practical computational methods can be developed to approximate and evaluate the contributions of the resulting stochastic expressions. We demonstrate our methods on several examples, including time-varying SDEs that arise in particle simulations and for SPDEs that model fluctuations in concentration fields of spatially-extended systems. Our introduced approaches provide methods for preserving statistical structures and other properties to obtain exponential numerical integrators for handling stiffness in time-varying stochastic dynamical systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135034"},"PeriodicalIF":2.9,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527012","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}
In this paper, we address the long-time asymptotic behavior of the generalized coupled high-order nonlinear Schrödinger (gCH-NLS) equation with initial data in Schwartz space that can support solitons. We construct the corresponding Riemann–Hilbert (RH) problem based on the spectral analysis of the associated 3 × 3 matrix Lax pair. By eliminating discrete spectral singularities through the Darboux transformation, we transform the original RH problem into a new RH problem without poles. Employing the nonlinear steepest-descent method for RH problems, as introduced by Deift and Zhou, we derive the long-time asymptotic expansion of the solution , achieving a residual error on the order of , where . Notably, our results can directly derive the long-time asymptotic behavior with soliton of both the fourth-order dispersive nonlinear Schrödinger equation and the coupled high-order nonlinear Schrödinger systems as special cases.
{"title":"Long-time asymptotic behavior of the generalized coupled high-order nonlinear Schrödinger equation with solitons","authors":"Wenxia Chen , Chaosheng Zhang , Boling Guo , Lixin Tian","doi":"10.1016/j.physd.2025.135017","DOIUrl":"10.1016/j.physd.2025.135017","url":null,"abstract":"<div><div>In this paper, we address the long-time asymptotic behavior of the generalized coupled high-order nonlinear Schrödinger (gCH-NLS) equation with initial data in Schwartz space <span><math><mrow><mi>S</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span> that can support solitons. We construct the corresponding Riemann–Hilbert (RH) problem based on the spectral analysis of the associated 3 × 3 matrix Lax pair. By eliminating discrete spectral singularities through the Darboux transformation, we transform the original RH problem into a new RH problem without poles. Employing the nonlinear steepest-descent method for RH problems, as introduced by Deift and Zhou, we derive the long-time asymptotic expansion of the solution <span><math><mrow><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span>, achieving a residual error on the order of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>p</mi></mrow></mfrac></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><mn>2</mn><mo>≤</mo><mi>p</mi><mo><</mo><mi>∞</mi></mrow></math></span>. Notably, our results can directly derive the long-time asymptotic behavior with soliton of both the fourth-order dispersive nonlinear Schrödinger equation and the coupled high-order nonlinear Schrödinger systems as special cases.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135017"},"PeriodicalIF":2.9,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527011","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 : 2025-11-11DOI: 10.1016/j.physd.2025.134982
Elizaveta Soboleva, Semyon Rudyi, Dmitrii Shcherbinin, Andrei Ivanov
We propose an optomechanical system that can be used as a platform for an Ising machine featuring controllable spatial bifurcation. The system is based on a hybrid surface trap for charged particles, consisting of a planar electrode structure and a laser beam directed perpendicular to the electrode surface. This configuration exhibits bistable dynamics with a pitchfork-type bifurcation between stable particle localization points. We establish the functional dependence of bifurcation parameter on physical system parameters, including electrode geometry, electrodynamic field characteristics, particle properties, and laser power. The system dynamics is analyzed in two scenarios: under compensation of optical radiation pressure and gravitational forces, and without such compensation. Bifurcation control is achieved by tuning the laser intensity. A one-dimensional effective potential model of the system has been described in terms of Duffing potential.
{"title":"Controllable spatial bifurcation in optomechanical system: Analytical and numerical study","authors":"Elizaveta Soboleva, Semyon Rudyi, Dmitrii Shcherbinin, Andrei Ivanov","doi":"10.1016/j.physd.2025.134982","DOIUrl":"10.1016/j.physd.2025.134982","url":null,"abstract":"<div><div>We propose an optomechanical system that can be used as a platform for an Ising machine featuring controllable spatial bifurcation. The system is based on a hybrid surface trap for charged particles, consisting of a planar electrode structure and a laser beam directed perpendicular to the electrode surface. This configuration exhibits bistable dynamics with a pitchfork-type bifurcation between stable particle localization points. We establish the functional dependence of bifurcation parameter on physical system parameters, including electrode geometry, electrodynamic field characteristics, particle properties, and laser power. The system dynamics is analyzed in two scenarios: under compensation of optical radiation pressure and gravitational forces, and without such compensation. Bifurcation control is achieved by tuning the laser intensity. A one-dimensional effective potential model of the system has been described in terms of Duffing potential.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 134982"},"PeriodicalIF":2.9,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145576962","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 : 2025-11-11DOI: 10.1016/j.physd.2025.134992
Samuel M. Nuugulu , Kailash C. Patidar , Divine T. Tarla
This paper presents two data driven approaches, the purely data driven (PDD) and physics informed neural network (PINN) approach for solving asset pricing problems. The PDD approach relies purely on available data and does not require any governing partial differential equation (PDE) to solve a pricing problem. On the other hand, under the PINN approach, the pricing is done by solving a governing PDE. Both models are calibrated to observed market prices, and their implied volatilities are compared to those derived from market data and the classical Black–Scholes model. The absolute errors and maximum absolute errors metrics relative to observed implied volatilities and prices and the prices obtained from the classical Black–Scholes model were used in measuring the goodness-of-fit of the two proposed techniques. Several hyperparameter tuning techniques were employed to optimize the performance of the two methods. In addition, we analyze the probability density functions (PDFs) derived from each method and verify that they are valid by demonstrating positivity and proper normalization. Theoretical results, including propositions and theorems, are presented to establish conditions under which the PINN, trained using the Adam optimizer and initialized via the Xavier method, converges to an optimal solution, i.e., a set of trainable parameters that minimize the loss function. In further extensions, the PINN approach was applied to pricing European put options under a Heston stochastic volatility model (HSVM) model. While both methods exhibit competitive performance when calibrated, our empirical findings indicate that the PINN approach yields superior accuracy and stability.
{"title":"Data driven neural network approaches for pricing options","authors":"Samuel M. Nuugulu , Kailash C. Patidar , Divine T. Tarla","doi":"10.1016/j.physd.2025.134992","DOIUrl":"10.1016/j.physd.2025.134992","url":null,"abstract":"<div><div>This paper presents two data driven approaches, the purely data driven (PDD) and physics informed neural network (PINN) approach for solving asset pricing problems. The PDD approach relies purely on available data and does not require any governing partial differential equation (PDE) to solve a pricing problem. On the other hand, under the PINN approach, the pricing is done by solving a governing PDE. Both models are calibrated to observed market prices, and their implied volatilities are compared to those derived from market data and the classical Black–Scholes model. The absolute errors and maximum absolute errors metrics relative to observed implied volatilities and prices and the prices obtained from the classical Black–Scholes model were used in measuring the goodness-of-fit of the two proposed techniques. Several hyperparameter tuning techniques were employed to optimize the performance of the two methods. In addition, we analyze the probability density functions (PDFs) derived from each method and verify that they are valid by demonstrating positivity and proper normalization. Theoretical results, including propositions and theorems, are presented to establish conditions under which the PINN, trained using the Adam optimizer and initialized via the Xavier method, converges to an optimal solution, i.e., a set of trainable parameters that minimize the loss function. In further extensions, the PINN approach was applied to pricing European put options under a Heston stochastic volatility model (HSVM) model. While both methods exhibit competitive performance when calibrated, our empirical findings indicate that the PINN approach yields superior accuracy and stability.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 134992"},"PeriodicalIF":2.9,"publicationDate":"2025-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527023","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 : 2025-11-10DOI: 10.1016/j.physd.2025.135030
Márcio Cavalcante , Ailton C. Nascimento
We study special regularity properties of solutions to the initial–boundary value problem associated with the Korteweg–de Vries equations posed on the positive half-line. In particular, for initial data and boundary data , where the restriction of to some subset of has an extra regularity for any , we prove that the regularity of solutions moves with infinite speed to its left as time evolves until a certain time . The existence of a stopping time appears because of the effect of the boundary function . Also, as a consequence of our proof, we prove a gain in the regularity of the trace derivatives of the solutions for the Korteweg–de Vries on the half-line.
{"title":"On the propagation of regularity of solutions to the KdV equation on the positive half-line","authors":"Márcio Cavalcante , Ailton C. Nascimento","doi":"10.1016/j.physd.2025.135030","DOIUrl":"10.1016/j.physd.2025.135030","url":null,"abstract":"<div><div>We study special regularity properties of solutions to the initial–boundary value problem associated with the Korteweg–de Vries equations posed on the positive half-line. In particular, for initial data <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></mrow></mrow></math></span> and boundary data <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><msup><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mo>+</mo></mrow></msup></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></mrow></mrow></math></span>, where the restriction of <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> to some subset of <span><math><mrow><mo>(</mo><mi>b</mi><mo>,</mo><mi>∞</mi><mo>)</mo></mrow></math></span> has an extra regularity for any <span><math><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow></math></span>, we prove that the regularity of solutions <span><math><mi>u</mi></math></span> moves with infinite speed to its left as time evolves until a certain time <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>. The existence of a stopping time <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> appears because of the effect of the boundary function <span><math><mi>f</mi></math></span>. Also, as a consequence of our proof, we prove a gain in the regularity of the trace derivatives of the solutions for the Korteweg–de Vries on the half-line.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135030"},"PeriodicalIF":2.9,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527014","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 : 2025-11-10DOI: 10.1016/j.physd.2025.135032
R. Camassa , G. Falqui , G. Ortenzi , M. Pedroni
Collapse of a cavity, or a depression hollow, in a water layer under gravity is modeled with the so-called Shallow Water equations in three dimensional settings, under circular symmetry and its deformation to elliptical cross sections. Self-similar, explicit solutions are found by quadratures in terms of elliptic integrals. We show that the presence of a rigid floor and the proximity of the cavity to this boundary significantly affects the evolution of the free surface, with the collapse evolving to form jet pairs originating at the caustics locations determined by the initial ellipsoidal cavity. The loss of symmetry implied by the deformation to elliptical cross sectional shapes leads to time evolution governed by an integrable two-degree of freedom Hamiltonian system. It is shown that the formation of the singularities is a reflection of the different critical exponents of the fluid velocity components in the solutions, with only the component aligned with the minor axis exhibiting a gradient catastrophe in finite time.
{"title":"Gravitational collapse of liquid layer cavities near boundaries","authors":"R. Camassa , G. Falqui , G. Ortenzi , M. Pedroni","doi":"10.1016/j.physd.2025.135032","DOIUrl":"10.1016/j.physd.2025.135032","url":null,"abstract":"<div><div>Collapse of a cavity, or a depression hollow, in a water layer under gravity is modeled with the so-called Shallow Water equations in three dimensional settings, under circular symmetry and its deformation to elliptical cross sections. Self-similar, explicit solutions are found by quadratures in terms of elliptic integrals. We show that the presence of a rigid floor and the proximity of the cavity to this boundary significantly affects the evolution of the free surface, with the collapse evolving to form jet pairs originating at the caustics locations determined by the initial ellipsoidal cavity. The loss of symmetry implied by the deformation to elliptical cross sectional shapes leads to time evolution governed by an integrable two-degree of freedom Hamiltonian system. It is shown that the formation of the singularities is a reflection of the different critical exponents of the fluid velocity components in the solutions, with only the component aligned with the minor axis exhibiting a gradient catastrophe in finite time.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135032"},"PeriodicalIF":2.9,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527021","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 : 2025-11-10DOI: 10.1016/j.physd.2025.135033
Ruixiang Jia, Yulong Bai, Wenbin Yue, Xiaoxin Yue
Enhancing the robustness and accuracy of data assimilation (DA) systems is crucial for reliable state estimation in high-dimensional, nonlinear dynamical environments, where classical ensemble-based approaches often suffer from spurious long-range correlations and limited adaptability to multiscale dynamics. To address these challenges, this study introduces EnTLHF-RL, an improved filtering framework that incorporates spatial localization into the Ensemble Time-Localized H∞ Filter (EnTLHF). The proposed approach employs a correlation-based localization matrix to attenuate cross-variable correlations induced by finite-ensemble effects, while simultaneously introducing dynamic observation error estimation and quality control, thereby reinforcing spatial locality, enhancing numerical stability, and strengthening the overall reliability and adaptability of the assimilation framework. This design improves both the robustness and adaptability of the filter in regimes characterized by strong nonlinearity and chaotic behavior. The method is evaluated using Observing System Simulation Experiments (OSSEs) on two representative benchmark models: the Lorenz-96 system, under varying levels of dynamical forcing, and the Kuramoto–Sivashinsky (KS) equation, which exemplifies high-dimensional spatiotemporal chaos. Across both systems, EnTLHF-RL demonstrates superior performance over Ensemble Kalman Filter (EnKF) and EnTLHF, yielding lower root mean square errors and improved long-term stability. These results highlight the method’s potential as a robust and scalable assimilation framework for nonlinear physical systems under uncertainty.
{"title":"A robust ensemble time-localization H-infinity filter for chaotic dynamical models","authors":"Ruixiang Jia, Yulong Bai, Wenbin Yue, Xiaoxin Yue","doi":"10.1016/j.physd.2025.135033","DOIUrl":"10.1016/j.physd.2025.135033","url":null,"abstract":"<div><div>Enhancing the robustness and accuracy of data assimilation (DA) systems is crucial for reliable state estimation in high-dimensional, nonlinear dynamical environments, where classical ensemble-based approaches often suffer from spurious long-range correlations and limited adaptability to multiscale dynamics. To address these challenges, this study introduces EnTLHF-RL, an improved filtering framework that incorporates spatial localization into the Ensemble Time-Localized H∞ Filter (EnTLHF). The proposed approach employs a correlation-based localization matrix to attenuate cross-variable correlations induced by finite-ensemble effects, while simultaneously introducing dynamic observation error estimation and quality control, thereby reinforcing spatial locality, enhancing numerical stability, and strengthening the overall reliability and adaptability of the assimilation framework. This design improves both the robustness and adaptability of the filter in regimes characterized by strong nonlinearity and chaotic behavior. The method is evaluated using Observing System Simulation Experiments (OSSEs) on two representative benchmark models: the Lorenz-96 system, under varying levels of dynamical forcing, and the Kuramoto–Sivashinsky (KS) equation, which exemplifies high-dimensional spatiotemporal chaos. Across both systems, EnTLHF-RL demonstrates superior performance over Ensemble Kalman Filter (EnKF) and EnTLHF, yielding lower root mean square errors and improved long-term stability. These results highlight the method’s potential as a robust and scalable assimilation framework for nonlinear physical systems under uncertainty.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135033"},"PeriodicalIF":2.9,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527022","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 : 2025-11-08DOI: 10.1016/j.physd.2025.135016
Ziqi Ren , Xingwu Chen
As a complement to DC–DC buck converters investigated in previous publications, in this paper we analyze the dynamics of a 3-dimensional Filippov system arising from a DC–DC boost converter, including the singular point bifurcation and the existence of crossing limit cycles. This system has two intersected tangency lines on the switching boundary, which leads to more complicated dynamical behaviors than the buck converter because the latter has two parallel tangency lines. We obtain stability conditions for the intersection point of these two tangency lines in sliding regions and bifurcation conditions for it dividing into several singular points such as standard equilibria, boundary equilibria, cusps, and prove the existence of crossing limit cycles by pseudo-Hopf bifurcations. Finally, our main results are applied to this DC–DC boost converter to explain the reason of boost failure, to find critical parameter values leading to boost failure, to provide strategies for keeping the boost function even if some electrical apparatus elements are changed.
{"title":"Bifurcations and crossing limit cycles of a Filippov system arising from a DC–DC boost converter","authors":"Ziqi Ren , Xingwu Chen","doi":"10.1016/j.physd.2025.135016","DOIUrl":"10.1016/j.physd.2025.135016","url":null,"abstract":"<div><div>As a complement to DC–DC buck converters investigated in previous publications, in this paper we analyze the dynamics of a 3-dimensional Filippov system arising from a DC–DC boost converter, including the singular point bifurcation and the existence of crossing limit cycles. This system has two intersected tangency lines on the switching boundary, which leads to more complicated dynamical behaviors than the buck converter because the latter has two parallel tangency lines. We obtain stability conditions for the intersection point of these two tangency lines in sliding regions and bifurcation conditions for it dividing into several singular points such as standard equilibria, boundary equilibria, cusps, and prove the existence of crossing limit cycles by pseudo-Hopf bifurcations. Finally, our main results are applied to this DC–DC boost converter to explain the reason of boost failure, to find critical parameter values leading to boost failure, to provide strategies for keeping the boost function even if some electrical apparatus elements are changed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135016"},"PeriodicalIF":2.9,"publicationDate":"2025-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527025","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 : 2025-11-05DOI: 10.1016/j.physd.2025.135018
Zhaoquan Xu , Dongmei Xiao , Chufen Wu
We investigate the traveling wave dynamics in a population model with mobile and stationary states under a changing environment, which is modeled by a partially degenerate reaction–diffusion equation with a moving variable , . We focus on whether the species could keep up with the changing environment, that is, whether the equation model has a forced traveling wave with speed , and how the switching rates between mobile and stationary states affect the propagation dynamics. It is shown that there exists a threshold value , such that the equation model admits a forced traveling wave with speed if and only if the environment shifting speed . Thereby, the species cannot follow the changing environment with speed if . Compared to the well-known results on the classic Fisher’s equation which assumes the population has only mobile state, our result highlights a significant observation: the presence of stationary state in population will reduce the invasion threshold value . Moreover, it is proved that such a forced traveling wave is unique and globally stable if . This implies that the species can successfully invade new environment as a forced wave if the environment shifting speed satisfies . Some numerical simulations are also provided to illustrate the theoretical results and explain the invasion phenomena of species under environmental changes.
{"title":"Forced traveling waves in a population model with mobile and stationary states under a changing environment","authors":"Zhaoquan Xu , Dongmei Xiao , Chufen Wu","doi":"10.1016/j.physd.2025.135018","DOIUrl":"10.1016/j.physd.2025.135018","url":null,"abstract":"<div><div>We investigate the traveling wave dynamics in a population model with mobile and stationary states under a changing environment, which is modeled by a partially degenerate reaction–diffusion equation with a moving variable <span><math><mrow><mi>x</mi><mo>+</mo><mi>c</mi><mi>t</mi></mrow></math></span>, <span><math><mrow><mi>c</mi><mo>∈</mo><mi>R</mi></mrow></math></span>. We focus on whether the species could keep up with the changing environment, that is, whether the equation model has a forced traveling wave with speed <span><math><mi>c</mi></math></span>, and how the switching rates between mobile and stationary states affect the propagation dynamics. It is shown that there exists a threshold value <span><math><mrow><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>></mo><mn>0</mn></mrow></math></span>, such that the equation model admits a forced traveling wave with speed <span><math><mi>c</mi></math></span> if and only if the environment shifting speed <span><math><mrow><mi>c</mi><mo>></mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Thereby, the species cannot follow the changing environment with speed <span><math><mi>c</mi></math></span> if <span><math><mrow><mi>c</mi><mo>≤</mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Compared to the well-known results on the classic Fisher’s equation which assumes the population has only mobile state, our result highlights a significant observation: the presence of stationary state in population will reduce the invasion threshold value <span><math><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>. Moreover, it is proved that such a forced traveling wave is unique and globally stable if <span><math><mrow><mi>c</mi><mo>></mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. This implies that the species can successfully invade new environment as a forced wave if the environment shifting speed <span><math><mi>c</mi></math></span> satisfies <span><math><mrow><mi>c</mi><mo>></mo><mo>−</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Some numerical simulations are also provided to illustrate the theoretical results and explain the invasion phenomena of species under environmental changes.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135018"},"PeriodicalIF":2.9,"publicationDate":"2025-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475980","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}
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