Pub Date : 2025-11-20DOI: 10.1016/j.physd.2025.135052
Farangis Mahdizadeh Ghohe, Leila N. Azadani
Turbulent flow of non-Newtonian fluids is common in daily life and engineering practice. Unlike Newtonian fluids, non-Newtonian fluids have a viscosity that depends on time or shear rate, complicating their behavior, especially in turbulent regime. Large Eddy Simulation (LES) with Subgrid Scale (SGS) models such as standard Smagorinsky, dynamic Smagorinsky, and scale-dependent dynamic Smagorinsky has shown promise for simulating turbulent flows of Newtonian fluids. However, the application of these models, particularly the scale-dependent dynamic Smagorinsky model, to turbulent flows of non-Newtonian fluids remains largely unexplored. This paper investigated the robustness of the scale-dependent dynamic Smagorinsky model in LES of the turbulent non-Newtonian Burgers’ equation. Results for velocity and energy spectrum from the standard Smagorinsky, dynamic Smagorinsky, and scale-dependent dynamic Smagorinsky models were compared against Direct Numerical Simulation (DNS). It was demonstrated that the scale-dependent dynamic Smagorinsky model performs better than both the standard and dynamic Smagorinsky models in simulating turbulent flow of non-Newtonian fluids.
{"title":"Applying the scale-dependent dynamic Smagorinsky model in large eddy simulation of the turbulent non-Newtonian Burgers’ equation","authors":"Farangis Mahdizadeh Ghohe, Leila N. Azadani","doi":"10.1016/j.physd.2025.135052","DOIUrl":"10.1016/j.physd.2025.135052","url":null,"abstract":"<div><div>Turbulent flow of non-Newtonian fluids is common in daily life and engineering practice. Unlike Newtonian fluids, non-Newtonian fluids have a viscosity that depends on time or shear rate, complicating their behavior, especially in turbulent regime. Large Eddy Simulation (LES) with Subgrid Scale (SGS) models such as standard Smagorinsky, dynamic Smagorinsky, and scale-dependent dynamic Smagorinsky has shown promise for simulating turbulent flows of Newtonian fluids. However, the application of these models, particularly the scale-dependent dynamic Smagorinsky model, to turbulent flows of non-Newtonian fluids remains largely unexplored. This paper investigated the robustness of the scale-dependent dynamic Smagorinsky model in LES of the turbulent non-Newtonian Burgers’ equation. Results for velocity and energy spectrum from the standard Smagorinsky, dynamic Smagorinsky, and scale-dependent dynamic Smagorinsky models were compared against Direct Numerical Simulation (DNS). It was demonstrated that the scale-dependent dynamic Smagorinsky model performs better than both the standard and dynamic Smagorinsky models in simulating turbulent flow of non-Newtonian fluids.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"485 ","pages":"Article 135052"},"PeriodicalIF":2.9,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616269","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 : 2025-11-17DOI: 10.1016/j.physd.2025.135031
Amadeu Delshams , Mercè Ollé , Juan Ramon Pacha , Óscar Rodríguez
We consider the Rydberg electron in a circularly polarized microwave field, whose dynamics is described by a 2 d.o.f. Hamiltonian, which is a perturbation of size of the standard rotating Kepler problem. In a rotating frame, the largest chaotic region of this system lies around a saddle–center equilibrium point and its associated invariant manifolds. We compute the distance between stable and unstable manifolds of by means of a semi-analytical method, which consists of combining normal form, Melnikov, and averaging methods with numerical methods performed with multiple precision computations. Also, we introduce a new family of Hamiltonians, which we call Toy CP systems, to be able to compare our numerical results with the existing theoretical results in the literature. It should be noted that the distance between these stable and unstable manifolds is exponentially small in the perturbation parameter (in analogy with the libration point of the R3BP).
{"title":"Breakdown of homoclinic orbits to L1 of the hydrogen atom in a circularly polarized microwave field","authors":"Amadeu Delshams , Mercè Ollé , Juan Ramon Pacha , Óscar Rodríguez","doi":"10.1016/j.physd.2025.135031","DOIUrl":"10.1016/j.physd.2025.135031","url":null,"abstract":"<div><div>We consider the Rydberg electron in a circularly polarized microwave field, whose dynamics is described by a 2 d.o.f. Hamiltonian, which is a perturbation of size <span><math><mrow><mi>K</mi><mo>></mo><mn>0</mn></mrow></math></span> of the standard rotating Kepler problem. In a rotating frame, the largest chaotic region of this system lies around a saddle–center equilibrium point <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and its associated invariant manifolds. We compute the distance between stable and unstable manifolds of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> by means of a semi-analytical method, which consists of combining normal form, Melnikov, and averaging methods with numerical methods performed with multiple precision computations. Also, we introduce a new family of Hamiltonians, which we call <em>Toy CP systems</em>, to be able to compare our numerical results with the existing theoretical results in the literature. It should be noted that the distance between these stable and unstable manifolds is exponentially small in the perturbation parameter <span><math><mi>K</mi></math></span> (in analogy with the <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> libration point of the R3BP).</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"485 ","pages":"Article 135031"},"PeriodicalIF":2.9,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145578349","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 : 2025-11-15DOI: 10.1016/j.physd.2025.135040
Man-Hong Fan , Jun-Hao Zhao , Lin Ding , Xiao-Ying Ma
The traditional methods for forecasting nonlinear dynamics problems rely mainly on experimental means and numerical simulations; however, both methods struggle to address high-order complex dynamic issues. Physics-informed neural networks (PINNs) have been extensively applied to predict partial differential equations (PDEs) and can be used to simulate physical systems. Nevertheless, when their solutions exhibit high-dimensional nonlinear characteristics, the accuracy of PINNs can decrease significantly. To enhance the predictive capability of PINNs for high-order complex dynamical systems, this study proposes a novel PINNs architecture integrated with Residual Network (ResNet) blocks. The framework addresses critical challenges such as gradient vanishing through identity mappings when employing deep network structures, thereby enabling effective capture of rapidly varying solutions in physical fields. To validate the performance of the PINNs with ResNet blocks, numerical experiments are conducted on the chaotic Lorenz system, the Kuramoto-Sivashinsky equation in a chaotic state, and the Navier-Stokes equation. These results are compared with those obtained using a PINNs framework that is based on multilayer perceptrons (MLPs). The results indicate that the PINNs with ResNet blocks exhibit stronger prediction capabilities and robustness than the PINNs framework based on MLPs.
{"title":"Forecasting of spatiotemporal nonlinear dynamic systems by Physics-informed neural networks with ResNet blocks","authors":"Man-Hong Fan , Jun-Hao Zhao , Lin Ding , Xiao-Ying Ma","doi":"10.1016/j.physd.2025.135040","DOIUrl":"10.1016/j.physd.2025.135040","url":null,"abstract":"<div><div>The traditional methods for forecasting nonlinear dynamics problems rely mainly on experimental means and numerical simulations; however, both methods struggle to address high-order complex dynamic issues. Physics-informed neural networks (PINNs) have been extensively applied to predict partial differential equations (PDEs) and can be used to simulate physical systems. Nevertheless, when their solutions exhibit high-dimensional nonlinear characteristics, the accuracy of PINNs can decrease significantly. To enhance the predictive capability of PINNs for high-order complex dynamical systems, this study proposes a novel PINNs architecture integrated with Residual Network (ResNet) blocks. The framework addresses critical challenges such as gradient vanishing through identity mappings when employing deep network structures, thereby enabling effective capture of rapidly varying solutions in physical fields. To validate the performance of the PINNs with ResNet blocks, numerical experiments are conducted on the chaotic Lorenz system, the Kuramoto-Sivashinsky equation in a chaotic state, and the Navier-Stokes equation. These results are compared with those obtained using a PINNs framework that is based on multilayer perceptrons (MLPs). The results indicate that the PINNs with ResNet blocks exhibit stronger prediction capabilities and robustness than the PINNs framework based on MLPs.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"485 ","pages":"Article 135040"},"PeriodicalIF":2.9,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145578350","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 : 2025-11-15DOI: 10.1016/j.physd.2025.135038
Iacopo P. Longo , Rafael Obaya , Ana M. Sanz
Starting from a classical Budyko–Sellers–Ghil energy balance model for the average surface temperature of the Earth, a nonautonomous version is designed by allowing the solar irradiance and the cloud cover coefficients to vary with time on a fast timescale, and to exhibit chaos in a precise sense. The dynamics of this model is described in terms of three existing nonautonomous equilibria, the upper one being attracting and representing the present temperature profile. The theory of averaging is used to compare the nonautonomous model and its time-averaged version. We analyse the influence of the qualitative properties of the time-dependent coefficients and obtain reasonable approximations close to the upper hyperbolic solution. Furthermore, previous concepts of two-point response and sensitivity functions are adapted to the nonautonomous context and used to value the increase in temperature when a forcing caused by CO and other emissions intervenes.
{"title":"Nonautonomous modelling in energy balance models of climate. Limitations of averaging and climate sensitivity","authors":"Iacopo P. Longo , Rafael Obaya , Ana M. Sanz","doi":"10.1016/j.physd.2025.135038","DOIUrl":"10.1016/j.physd.2025.135038","url":null,"abstract":"<div><div>Starting from a classical Budyko–Sellers–Ghil energy balance model for the average surface temperature of the Earth, a nonautonomous version is designed by allowing the solar irradiance and the cloud cover coefficients to vary with time on a fast timescale, and to exhibit chaos in a precise sense. The dynamics of this model is described in terms of three existing nonautonomous equilibria, the upper one being attracting and representing the present temperature profile. The theory of averaging is used to compare the nonautonomous model and its time-averaged version. We analyse the influence of the qualitative properties of the time-dependent coefficients and obtain reasonable approximations close to the upper hyperbolic solution. Furthermore, previous concepts of two-point response and sensitivity functions are adapted to the nonautonomous context and used to value the increase in temperature when a forcing caused by CO<span><math><msub><mrow></mrow><mrow><mn>2</mn></mrow></msub></math></span> and other emissions intervenes.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"485 ","pages":"Article 135038"},"PeriodicalIF":2.9,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145578388","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 : 2025-11-15DOI: 10.1016/j.physd.2025.135037
Rafael de la Rosa, Elena Medina
<div><div>The survival of a population confined within a bounded habitat is a classical problem, traditionally analyzed in terms of the habitat size. In the linear case, persistence is ensured when the domain length exceeds a critical size <span><math><msub><mrow><mi>l</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>. In nonlinear models, however survival conditions become considerably more complex and may even take less intuitive forms, such as <span><math><mrow><mi>l</mi><mspace></mspace><mo>≤</mo><mspace></mspace><msub><mrow><mi>l</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math></span>. In this context, Colombo and Anteneodo (2018) studied the power-law reaction–diffusion model <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mspace></mspace><mo>=</mo><mspace></mspace><mi>D</mi><mspace></mspace><msub><mrow><mrow><mo>(</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>ν</mi><mo>−</mo><mn>1</mn></mrow></msup><mspace></mspace><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>x</mi></mrow></msub><mspace></mspace><mo>+</mo><mspace></mspace><mi>a</mi><mspace></mspace><msup><mrow><mi>u</mi></mrow><mrow><mi>μ</mi></mrow></msup></mrow></math></span>, with <span><math><mrow><mi>μ</mi><mo>,</mo><mi>ν</mi><mo>></mo><mn>0</mn></mrow></math></span>, accompanied by hostile boundary conditions, determining survival thresholds in terms of habitat size for initially homogeneous populations.</div><div>In this paper, we propose a general formulation of the persistence question by rewriting the power-law reaction–diffusion model in terms of suitable nondimensional variables. This approach reveals that persistence can be naturally expressed through a parameter <span><math><mrow><mi>Q</mi><mo>≔</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>D</mi></mrow></mfrac><msup><mrow><mi>l</mi></mrow><mrow><mo>−</mo><mi>μ</mi><mo>+</mo><mi>ν</mi><mo>+</mo><mn>2</mn></mrow></msup><msubsup><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>μ</mi><mo>−</mo><mi>ν</mi></mrow></msubsup></mrow></math></span>. We show that there exists a critical value <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> depending on <span><math><mi>μ</mi></math></span>, <span><math><mi>ν</mi></math></span> and the initial distribution, such that survival occurs whenever <span><math><mrow><mi>Q</mi><mo>≥</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math></span>. This more intuitive condition reconciles the various survival criteria within a unified framework.</div><div>To further explore this condition, we analyze two one-parameter families of initial distributions, including the homogeneous case, and apply a finite-difference scheme to estimate <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>. Conversely, for given model parameters <span><math><mi>μ</mi></math></span>, <span><math><mi>ν</mi></math></span>, <span><math><mi>
{"title":"A general formulation of the survival problem in a power-law reaction–diffusion model: Emergence of a critical parameter","authors":"Rafael de la Rosa, Elena Medina","doi":"10.1016/j.physd.2025.135037","DOIUrl":"10.1016/j.physd.2025.135037","url":null,"abstract":"<div><div>The survival of a population confined within a bounded habitat is a classical problem, traditionally analyzed in terms of the habitat size. In the linear case, persistence is ensured when the domain length exceeds a critical size <span><math><msub><mrow><mi>l</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>. In nonlinear models, however survival conditions become considerably more complex and may even take less intuitive forms, such as <span><math><mrow><mi>l</mi><mspace></mspace><mo>≤</mo><mspace></mspace><msub><mrow><mi>l</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math></span>. In this context, Colombo and Anteneodo (2018) studied the power-law reaction–diffusion model <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mspace></mspace><mo>=</mo><mspace></mspace><mi>D</mi><mspace></mspace><msub><mrow><mrow><mo>(</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>ν</mi><mo>−</mo><mn>1</mn></mrow></msup><mspace></mspace><msub><mrow><mi>u</mi></mrow><mrow><mi>x</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>x</mi></mrow></msub><mspace></mspace><mo>+</mo><mspace></mspace><mi>a</mi><mspace></mspace><msup><mrow><mi>u</mi></mrow><mrow><mi>μ</mi></mrow></msup></mrow></math></span>, with <span><math><mrow><mi>μ</mi><mo>,</mo><mi>ν</mi><mo>></mo><mn>0</mn></mrow></math></span>, accompanied by hostile boundary conditions, determining survival thresholds in terms of habitat size for initially homogeneous populations.</div><div>In this paper, we propose a general formulation of the persistence question by rewriting the power-law reaction–diffusion model in terms of suitable nondimensional variables. This approach reveals that persistence can be naturally expressed through a parameter <span><math><mrow><mi>Q</mi><mo>≔</mo><mfrac><mrow><mi>a</mi></mrow><mrow><mi>D</mi></mrow></mfrac><msup><mrow><mi>l</mi></mrow><mrow><mo>−</mo><mi>μ</mi><mo>+</mo><mi>ν</mi><mo>+</mo><mn>2</mn></mrow></msup><msubsup><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>μ</mi><mo>−</mo><mi>ν</mi></mrow></msubsup></mrow></math></span>. We show that there exists a critical value <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> depending on <span><math><mi>μ</mi></math></span>, <span><math><mi>ν</mi></math></span> and the initial distribution, such that survival occurs whenever <span><math><mrow><mi>Q</mi><mo>≥</mo><msub><mrow><mi>Q</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math></span>. This more intuitive condition reconciles the various survival criteria within a unified framework.</div><div>To further explore this condition, we analyze two one-parameter families of initial distributions, including the homogeneous case, and apply a finite-difference scheme to estimate <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>. Conversely, for given model parameters <span><math><mi>μ</mi></math></span>, <span><math><mi>ν</mi></math></span>, <span><math><mi>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"485 ","pages":"Article 135037"},"PeriodicalIF":2.9,"publicationDate":"2025-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145578389","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 : 2025-11-13DOI: 10.1016/j.physd.2025.135036
Ricardo Chacón , Pedro J. Martínez
Jacobian elliptic functions have been at the heart of nonlinear science for two hundred years. Through the exploration of two biparametric () elliptic-based generalizations of the Metropolis–Stein–Stein (MSS) map, and , with and being Jacobian elliptic functions of parameter , we provide analytical and numerical evidence that solely varying the impulse per unit of amplitude of the periodic map functions, while keeping its amplitude constant, shifts the bifurcation amplitudes, including those corresponding to the onset and extinction of chaos, with respect to the case of the standard MSS map. The analyses of the Schwarzian derivative of the two elliptic maps indicate that a change of its sign from negative to positive as the shape parameter is increased from 0 to 1 only occurs for the map , while the corresponding routes orderchaos for both elliptic maps still follow Feigenbaum’s universality. We found that maximal extension of the state space wherein presents a positive Schwarzian derivative occurs at a single critical value of the shape parameter: . Remarkably, this value corresponds to a magic universal waveform which optimally enhances directed ratchet transport by symmetry breaking and is associated with an enhancement of chaos for in parameter space with respect to the shift-symmetric map It should be emphasized that this change in the sign of the Schwarzian derivative is a genuine feature of the map which is completely absent in the standard MSS map.
{"title":"On some elliptic generalizations of the Metropolis–Stein–Stein map","authors":"Ricardo Chacón , Pedro J. Martínez","doi":"10.1016/j.physd.2025.135036","DOIUrl":"10.1016/j.physd.2025.135036","url":null,"abstract":"<div><div>Jacobian elliptic functions have been at the heart of nonlinear science for two hundred years. Through the exploration of two biparametric (<span><math><mrow><mi>λ</mi><mo>,</mo><mi>m</mi></mrow></math></span>) elliptic-based generalizations of the Metropolis–Stein–Stein (MSS) map, <span><math><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mo>sn</mo></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mo>sn</mo><mo>cn</mo></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>, with <span><math><mo>sn</mo></math></span> and <span><math><mo>cn</mo></math></span> being Jacobian elliptic functions of parameter <span><math><mi>m</mi></math></span>, we provide analytical and numerical evidence that solely varying the impulse per unit of amplitude of the periodic map functions, while keeping its amplitude <span><math><mi>λ</mi></math></span> constant, shifts the bifurcation amplitudes, including those corresponding to the onset and extinction of chaos, with respect to the case of the standard MSS map. The analyses of the Schwarzian derivative of the two elliptic maps indicate that a change of its sign from negative to positive as the shape parameter <span><math><mi>m</mi></math></span> is increased from 0 to 1 only occurs for the map <span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>sn</mo><mo>cn</mo></mrow></msub></math></span>, while the corresponding routes order<span><math><mo>↔</mo></math></span>chaos for both elliptic maps still follow Feigenbaum’s universality. We found that maximal extension of the state space wherein <span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>sn</mo><mo>cn</mo></mrow></msub></math></span> presents a positive Schwarzian derivative occurs at a single critical value of the shape parameter: <span><math><mrow><mi>m</mi><mo>=</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>≃</mo><mn>0</mn><mo>.</mo><mn>985682</mn></mrow></math></span>. Remarkably, this value corresponds to a magic universal waveform which optimally enhances directed ratchet transport by symmetry breaking and is associated with an enhancement of chaos for <span><math><mrow><mi>m</mi><mo>≲</mo><mn>1</mn></mrow></math></span> in parameter space with respect to the shift-symmetric map <span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>sn</mo></mrow></msub></math></span> It should be emphasized that this change in the sign of the Schwarzian derivative is a genuine feature of the map <span><math><msub><mrow><mi>f</mi></mrow><mrow><mo>sn</mo><mo>cn</mo></mrow></msub></math></span> which is completely absent in the standard MSS map.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"484 ","pages":"Article 135036"},"PeriodicalIF":2.9,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145527010","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 : 2025-11-13DOI: 10.1016/j.physd.2025.135035
Lianjie Song, Wei Liang, Qiu Du
A tri-neuron discrete-time BAM neural network with two delays is considered in this paper. When the network satisfies several relatively weak conditions, one criterion of stability is established. Moreover, proof of the existence of chaos in the sense of Li–Yorke and Devaney is given by applying the snap-back repeller theory. One example is demonstrated by showing its chaotic behavior and the trends of the largest Lyapunov exponent, which further illustrates the correctness of the obtained results.
{"title":"Dynamics analysis of a tri-neuron discrete-time BAM neural network with two delays","authors":"Lianjie Song, Wei Liang, Qiu Du","doi":"10.1016/j.physd.2025.135035","DOIUrl":"10.1016/j.physd.2025.135035","url":null,"abstract":"<div><div>A tri-neuron discrete-time BAM neural network with two delays is considered in this paper. When the network satisfies several relatively weak conditions, one criterion of stability is established. Moreover, proof of the existence of chaos in the sense of Li–Yorke and Devaney is given by applying the snap-back repeller theory. One example is demonstrated by showing its chaotic behavior and the trends of the largest Lyapunov exponent, which further illustrates the correctness of the obtained results.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"485 ","pages":"Article 135035"},"PeriodicalIF":2.9,"publicationDate":"2025-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145532546","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 : 2025-11-12DOI: 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}
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