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}
Pub Date : 2025-11-04DOI: 10.1016/j.physd.2025.135010
Rossella Della Marca , Alberto d’Onofrio , Carmelo F. Munafò , Romina Travaglini
In this work, in the context of a spatiotemporal Susceptible–Infectious–Removed (SIR) model with vaccination across all-ages, we consider the synergy between vaccine hesitancy and the intrinsic nonlocal spatial and temporal nature of the information used by agents to make their decisions.
First, we analytically investigate the stability of the spatially homogeneous endemic equilibrium: we prove that the proposed model has either Hopf instability or Turing instability, but it cannot have Turing–Hopf instability.
Second, we numerically show that, in the presence of both spatial and temporal nonlocality, the model may exhibit spatiotemporal quasi-periodicity. This phenomenon, to the best of our knowledge, was never been observed before in the context of behavioural epidemiology of infectious diseases. In other cases, instead, the triggering of other interesting spatiotemporal patterns is observed.
{"title":"Spatiotemporal quasiperiodicity induced by all-ages vaccine hesitancy in an SIR model","authors":"Rossella Della Marca , Alberto d’Onofrio , Carmelo F. Munafò , Romina Travaglini","doi":"10.1016/j.physd.2025.135010","DOIUrl":"10.1016/j.physd.2025.135010","url":null,"abstract":"<div><div>In this work, in the context of a spatiotemporal Susceptible–Infectious–Removed (SIR) model with vaccination across all-ages, we consider the synergy between vaccine hesitancy and the intrinsic nonlocal spatial and temporal nature of the information used by agents to make their decisions.</div><div>First, we analytically investigate the stability of the spatially homogeneous endemic equilibrium: we prove that the proposed model has either Hopf instability or Turing instability, but it cannot have Turing–Hopf instability.</div><div>Second, we numerically show that, in the presence of both spatial and temporal nonlocality, the model may exhibit spatiotemporal quasi-periodicity. This phenomenon, to the best of our knowledge, was never been observed before in the context of behavioural epidemiology of infectious diseases. In other cases, instead, the triggering of other interesting spatiotemporal patterns is observed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135010"},"PeriodicalIF":2.9,"publicationDate":"2025-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527013","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 : 2025-11-03DOI: 10.1016/j.physd.2025.135014
Hiroki Ono, Yusuke Doi, Akihiro Nakatani
We propose a novel type of umklapp-free lattice (UFL), where umklapp processes are completely absent. The proposed UFL incorporates cubic long-range nonlinearity, a feature not addressed in previous studies. In this paper, we derive an analytical expression for the cubic nonlinear coupling constants by imposing mathematical conditions such that the nonlinear coupling strength between particle pairs decays inversely with their separation distance. The absence of umklapp processes in the proposed lattice is confirmed through numerical comparisons with the Fermi–Pasta–Ulam–Tsingou (FPUT) lattice. Furthermore, molecular dynamics simulations are performed to investigate the thermal conductivity of the proposed lattice in the non-equilibrium steady state. Compared to the original FPUT lattice, the proposed UFL is closer to ballistic transport. Our results demonstrate that the umklapp processes induced by cubic nonlinearity are suppressed in the proposed UFL. Moreover, compared to the UFL with only quartic nonlinearity, truncation of long-range interactions plays a significant role in the proposed lattice.
{"title":"Construction of cubic nonlinear lattice free from umklapp processes","authors":"Hiroki Ono, Yusuke Doi, Akihiro Nakatani","doi":"10.1016/j.physd.2025.135014","DOIUrl":"10.1016/j.physd.2025.135014","url":null,"abstract":"<div><div>We propose a novel type of umklapp-free lattice (UFL), where umklapp processes are completely absent. The proposed UFL incorporates cubic long-range nonlinearity, a feature not addressed in previous studies. In this paper, we derive an analytical expression for the cubic nonlinear coupling constants by imposing mathematical conditions such that the nonlinear coupling strength between particle pairs decays inversely with their separation distance. The absence of umklapp processes in the proposed lattice is confirmed through numerical comparisons with the Fermi–Pasta–Ulam–Tsingou (FPUT) lattice. Furthermore, molecular dynamics simulations are performed to investigate the thermal conductivity of the proposed lattice in the non-equilibrium steady state. Compared to the original FPUT lattice, the proposed UFL is closer to ballistic transport. Our results demonstrate that the umklapp processes induced by cubic nonlinearity are suppressed in the proposed UFL. Moreover, compared to the UFL with only quartic nonlinearity, truncation of long-range interactions plays a significant role in the proposed lattice.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135014"},"PeriodicalIF":2.9,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475985","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 : 2025-11-01DOI: 10.1016/j.physd.2025.135015
Yi Hu, Jiang Yu
Piecewise systems are widely used to model real-world phenomena such as electrical circuits and neurons. Their rich dynamical behavior arises from two factors: the nonlinearity of the subsystems and the nonsmoothness induced by the switching curves. This article focuses on the latter factor. In particular, we consider an extended version of weak Hilbert’s 16th problem for some planar piecewise Hamiltonian systems. In these systems, the subsystems have fixed Hamiltonians, while the switching curves are perturbed in the family of curves. These systems reveal the exclusive influence of the switching curves. To study the influence, we provide the formula of the first order Melnikov function corresponding to the family of -crossing closed orbits and apply it to two problems.
In the first application, we investigate a system with linear subsystems and an algebraic switching curve of order , and prove that such systems have at least limit cycles. This improves the results of Douglas D. Novaes published in Physica D.
In the second application, we study a piecewise linear system with two subsystems and a hyperbola switching curve, and prove the existence of three crossing limit cycles that intersect the switching curve four times.
分段系统被广泛用于模拟现实世界的现象，如电路和神经元。其丰富的动力学行为源于两个因素：子系统的非线性和切换曲线引起的非光滑性。本文主要讨论后一个因素。特别地，我们考虑了一些平面分段哈密顿系统的弱Hilbert第16问题的扩展版本。在这些系统中，子系统具有固定的C1哈密顿量，而开关曲线在C1曲线族中是摄动的。这些系统揭示了开关曲线的独家影响。为了研究这种影响，我们给出了k交叉闭轨道族对应的一阶Melnikov函数的表达式，并将其应用于两个问题。在第一个应用中，我们研究了一个具有线性子系统和n阶代数切换曲线的系统，并证明了这样的系统至少有n个⌊n2⌋极限环。这改进了Douglas D. Novaes发表在《physics d》上的结果。在第二个应用中，我们研究了一个具有两个子系统和双曲线切换曲线的分段线性系统，并证明了与切换曲线相交四次的三个交叉极限环的存在性。
{"title":"Melnikov function of planar piecewise systems with a switching curve perturbed and its applications","authors":"Yi Hu, Jiang Yu","doi":"10.1016/j.physd.2025.135015","DOIUrl":"10.1016/j.physd.2025.135015","url":null,"abstract":"<div><div>Piecewise systems are widely used to model real-world phenomena such as electrical circuits and neurons. Their rich dynamical behavior arises from two factors: the nonlinearity of the subsystems and the nonsmoothness induced by the switching curves. This article focuses on the latter factor. In particular, we consider an extended version of weak Hilbert’s 16th problem for some planar piecewise Hamiltonian systems. In these systems, the subsystems have fixed <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> Hamiltonians, while the switching curves are perturbed in the family of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> curves. These systems reveal the exclusive influence of the switching curves. To study the influence, we provide the formula of the first order Melnikov function corresponding to the family of <span><math><mi>k</mi></math></span>-crossing closed orbits and apply it to two problems.</div><div>In the first application, we investigate a system with linear subsystems and an algebraic switching curve of order <span><math><mi>n</mi></math></span>, and prove that such systems have at least <span><math><mrow><mi>n</mi><mrow><mo>⌊</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo></mrow></mrow></math></span> limit cycles. This improves the results of Douglas D. Novaes published in Physica D.</div><div>In the second application, we study a piecewise linear system with two subsystems and a hyperbola switching curve, and prove the existence of three crossing limit cycles that intersect the switching curve four times.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135015"},"PeriodicalIF":2.9,"publicationDate":"2025-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145475984","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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