Physica D: Nonlinear Phenomena最新文献

{"title":"Spatial moment dynamics and biomass density equations provide complementary, yet limited, descriptions of pattern formation in individual-based simulations","authors":"Anudeep Surendran ,&nbsp;David Pinto-Ramos ,&nbsp;Rafael Menezes ,&nbsp;Ricardo Martinez-Garcia","doi":"10.1016/j.physd.2025.134703","DOIUrl":"10.1016/j.physd.2025.134703","url":null,"abstract":"<div><div>Spatial patterning is common in ecological systems and has been extensively studied via different modeling approaches. Individual-based models (IBMs) accurately describe nonlinear interactions at the organism level and the stochastic spatial dynamics that drives pattern formation, but their computational cost scales quickly with system complexity, limiting their practical use. Population-level approximations such as spatial moment dynamics (SMD)—which describe the moments of organism distributions—and coarse-grained biomass density models have been developed to address this limitation. However, the extent to which these approximated descriptions accurately capture the spatial patterns and population sizes emerging from individual-level simulations remains an open question. We investigate this issue considering a prototypical population dynamics IBM with long-range dispersal and intraspecific competition, for which we derive both its SMD and coarse-grained density approximations. We systematically compare the performance of these two approximations at predicting IBM population abundances and spatial patterns. Our results highlight that SMD and density-based approximations complement each other by correctly capturing these two population features within different parameter regimes. Importantly, we identify regions of the parameter space in which neither approximation performed well, which should encourage the development of more refined IBM approximation approaches.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134703"},"PeriodicalIF":2.7,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143917802","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}

{"title":"Global dynamics of a class of 3-dimensional piecewise linear observable system with two zones","authors":"Qian Tong,&nbsp;Shimin Li","doi":"10.1016/j.physd.2025.134678","DOIUrl":"10.1016/j.physd.2025.134678","url":null,"abstract":"<div><div>Piecewise smooth differential systems have garnered increasing attention due to their broad applications across various fields. Notably, existing literature primarily focuses on planar piecewise smooth systems. In this paper, we investigate a class of 3-dimensional piecewise linear homogeneous observable systems divided into two zones by a plane. We first establish the existence and stability of invariant cones, then analyze the dynamics on these cones utilizing properties of the Poincaré half map. Finally, through Poincaré compactification, we derive the global phase portraits within the Poincaré ball for this 3-dimensional system.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134678"},"PeriodicalIF":2.7,"publicationDate":"2025-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898468","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}

{"title":"Reservoir computing and non-linear dynamics for time series analysis: An application in the financial market","authors":"Francisco Alves dos Santos,&nbsp;Reneé Rodrigues Lima,&nbsp;Jerson Leite Alves,&nbsp;Davi Wanderley Misturini,&nbsp;Joao B. Florindo","doi":"10.1016/j.physd.2025.134698","DOIUrl":"10.1016/j.physd.2025.134698","url":null,"abstract":"<div><div>In various time series analysis scenarios, especially when some type of forecasting is intended, a pre-analysis of volatility, seasonality, and other data characteristics is recommended before the use of a forecasting model. This is a common scenario, for example, in the financial market. In this sense, this research aims to develop a mathematical-computational solution at two levels. In the first one, non-linear dynamics techniques are applied. These are incorporated here through the Hurst exponent, so that the series are grouped and combined with this measure. The purpose here is to extract different characteristic patterns present in this non-linear dynamics metric. Next, a reservoir computing (RC) model is applied to each combination independently, aiming to obtain a more robust general system capable of significantly improving its performance compared to the original RC model and other state-of-the-art predictive techniques. We expect that the proposed model will be able to extract information on long-term dependence, trends, as well as persistence and antipersistence patterns present in the data, which are incorporated through the Hurst exponents. Such additional information is employed here to improve the forecasting capacity of the model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134698"},"PeriodicalIF":2.7,"publicationDate":"2025-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143891927","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}

{"title":"Diffusive transport of a 2-D magnetized dusty plasma cloud","authors":"Aman Singh Katariya ,&nbsp;Amita Das ,&nbsp;Animesh Sharma ,&nbsp;Bibhuti Bhusan Sahu","doi":"10.1016/j.physd.2025.134692","DOIUrl":"10.1016/j.physd.2025.134692","url":null,"abstract":"<div><div>Transport across a transverse magnetic field of two-dimensional strongly coupled complex (dusty) plasma is studied using molecular dynamics simulations. In the collisionless undamped regime, the dust particles merely show radial pulsations in their position. This has been identified with the gyro motion of the dust particles. However, an additional damping process (which may arise due to dust-neutral collision) results in a diffusive transport. Detailed simulation studies have been carried out to obtain the scaling of the diffusion coefficient with respect to the magnetic field and the collision frequency. These scalings are found to be distinct for the two regimes of <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>c</mi><mi>d</mi></mrow></msub><mo>≪</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>d</mi><mi>n</mi></mrow></msub></mrow></math></span> and <span><math><mrow><msub><mrow><mi>ω</mi></mrow><mrow><mi>c</mi><mi>d</mi></mrow></msub><mo>≫</mo><msub><mrow><mi>ν</mi></mrow><mrow><mi>d</mi><mi>n</mi></mrow></msub></mrow></math></span>.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134692"},"PeriodicalIF":2.7,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898470","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}

{"title":"Kolmogorov–Smirnov estimation of self-similarity in long-range dependent fractional processes","authors":"Daniele Angelini,&nbsp;Sergio Bianchi","doi":"10.1016/j.physd.2025.134697","DOIUrl":"10.1016/j.physd.2025.134697","url":null,"abstract":"<div><div>This paper investigates the estimation of the self-similarity parameter in fractional processes. We re-examine the Kolmogorov–Smirnov (KS) test as a distribution-based method for assessing self-similarity, emphasizing its robustness and independence from specific probability distributions. Despite these advantages, the KS test encounters significant challenges when applied to fractional processes, primarily due to intrinsic data dependencies that induce both intradependent and interdependent effects. To address these limitations, we propose a novel method based on random permutation theory, which effectively removes autocorrelations while preserving the self-similarity structure of the process. Simulation results validate the robustness of the proposed approach, demonstrating its effectiveness in providing reliable estimation in the presence of strong dependencies. These findings establish a statistically rigorous framework for self-similarity analysis in fractional processes, with potential applications across various scientific domains.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134697"},"PeriodicalIF":2.7,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143903882","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}

{"title":"A family of μ-Camassa–Holm-type equations with peaked solutions","authors":"Hao Wang ,&nbsp;Kexin Yan ,&nbsp;Ying Fu","doi":"10.1016/j.physd.2025.134671","DOIUrl":"10.1016/j.physd.2025.134671","url":null,"abstract":"<div><div>In this paper, we present a general family of nonlinear dispersive wave equations, which can be regarded as a nonlocal counterpart of the <span><math><mrow><mi>f</mi><mi>g</mi></mrow></math></span>-family. We first show that the family of equations admits multi-peaked and single peaked solutions under certain conditions on two arbitrary functions. As typical subfamilies of the equations with peaked solutions, two generalized versions of the <span><math><mi>μ</mi></math></span>-Camassa–Holm and modified <span><math><mi>μ</mi></math></span>-Camassa–Holm equations are then proposed respectively, which preserve the Hamiltonian structure shared by the <span><math><mi>μ</mi></math></span>-Camassa–Holm and modified <span><math><mi>μ</mi></math></span>-Camassa–Holm equations. The peaked solutions and higher-order conserved densities are derived from these generalized equations. Furthermore, the interactions of two-peaked solutions are exhibited. It demonstrates that the higher-order nonlinearities have an impact on interactions of peaked solutions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134671"},"PeriodicalIF":2.7,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143882268","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}

{"title":"Local manifold approximation of dynamical system based on neural ordinary differential equation","authors":"Ya Xiao ,&nbsp;Zhixia Jiang ,&nbsp;Pinchao Meng ,&nbsp;Weishi Yin ,&nbsp;Dequan Qi ,&nbsp;Linhua Zhou","doi":"10.1016/j.physd.2025.134688","DOIUrl":"10.1016/j.physd.2025.134688","url":null,"abstract":"<div><div>In this paper, we present an innovative data-driven method that leverages the latest advancements in Neural Ordinary Differential Equations (NODEs) to learn dynamical system and perform local manifold approximation. This approach enables the capture of the underlying evolution mechanisms of complex nonlinear systems, even when only observational data is available. We first construct a NODE model, which is powered by a neural network, and then train it using the observational data to learn the vector field of the unknown nonlinear system. This allows for the approximation and prediction of its local manifold. We establish a universal approximation theorem for the local manifold approximation using NODEs, and through rigorous numerical experiments, we validate the method’s ability to approximate the local manifolds of nonlinear systems. In addition, we explore how factors such as network structure, complexity, and training data influence the approximation performance. Finally, we assess the robustness of NODE-based manifold approximation under various noisy conditions, demonstrating its generalization ability and resilience in real-world scenarios.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134688"},"PeriodicalIF":2.7,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143928429","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}

{"title":"Walking dynamics of a bipedal robot with impulsive actuation","authors":"Tengfei Long ,&nbsp;Xianfei Hui ,&nbsp;Guirong Jiang","doi":"10.1016/j.physd.2025.134677","DOIUrl":"10.1016/j.physd.2025.134677","url":null,"abstract":"<div><div>Impulsive actuation, which includes hip joint pulse torque and heel pulse thrust, is introduced to build a walking model of a bipedal robot on level ground in this study. The impulsive actuation configuration and the mechanism of stable walking motion are investigated. The existence and stability of period<span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> and 2 gaits are investigated by means of the discrete map. The conditions for flip bifurcation and inverse flip bifurcation of period<span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> gait are derived. The complex walking dynamics, such as period<span><math><mrow><mo>−</mo><mn>4</mn></mrow></math></span> gait, flip bifurcation and inverse flip bifurcation of period<span><math><mrow><mo>−</mo><mi>n</mi><mspace></mspace><mrow><mo>(</mo><mi>n</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></mrow></mrow></math></span> gait, and chaotic gait, are obtained by numerical simulations. By using period<span><math><mrow><mo>−</mo><mn>1</mn></mrow></math></span> gait, theoretical analysis is conducted on the energy consumption of applying pulse torque and constant torque to the hip joint under the same conditions. Numerical results show that the energy consumption of pulse torque is less than that of constant torque. The superiority and walking dynamics caused by impulsive actuation can provide theoretical reference for designing bipedal robots with stable and efficient walking.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134677"},"PeriodicalIF":2.7,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873849","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}

{"title":"Entanglement properties of photon–magnon crystal from nonlinear perspective","authors":"M. Wanic ,&nbsp;C. Jasiukiewicz ,&nbsp;Z. Toklikishvili ,&nbsp;V. Jandieri ,&nbsp;M. Trybus ,&nbsp;E. Jartych ,&nbsp;S.K. Mishra ,&nbsp;L. Chotorlishvili","doi":"10.1016/j.physd.2025.134699","DOIUrl":"10.1016/j.physd.2025.134699","url":null,"abstract":"<div><div>Quantifying the entanglement between two continuous bosonic modes, such as magnons and photons, is not trivial. The state-of-the-art for today is the logarithmic negativity, calculated through the quantum Langevin equations subjected to thermal noise. However, due to its complexity, this method requires further approximation. Namely, after the linearization procedure, quantum operators are replaced by their semiclassical expectation values calculated near the steady state. However, the phase space of a generic nonlinear system contains topologically different regions, and the steady state may correspond to the different types of fixed points, such as Saddle Points, Stable or unstable Spirals, and Nodes. Through the conventional linearization procedure, one obtains equations for the photon and magnon number operators, but the character of the fixed point is unexplored. In the present work, we propose a new procedure. Namely, we derived the complete set of nonlinear equations, which includes equations for the magnon and photon number operators and phases. We show that not only number operators but also phases are important for exploring the character of the fixed point, and the character of the fixed point influences the magnon–photon entanglement. We showed that methods of the qualitative theory of nonlinear differential equations are also relevant for photon–magnon entanglement problems. Our main finding is that entanglement is not defined in the Saddle Point region. On the other hand, the maximum of the entanglement corresponds to the region near the border between the Stable node and Stable spiral regions. Our approach is quite general. However, we did calculations for a particular system: photon–magnon crystal based on the yttrium iron garnet (YIG) film with the periodic air holes drilled in the film. Our interest focuses on magnons with a particular wavelength and frequency corresponding to the magnon condensate. Those magnons couple strongly with the photons of similar frequency. We discuss in detail the interaction between magnons and photons originating from the magneto-electric coupling and the effective Dzyaloshinskii–Moriya interaction. We show that this interaction is responsible for the robust photon–magnon entanglement in the system.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134699"},"PeriodicalIF":2.7,"publicationDate":"2025-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873848","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}

{"title":"Combined multi-scale-variational approach for finding quadratic three-color optical solitons at three-wave cascaded interaction","authors":"Vyacheslav A. Trofimov ,&nbsp;Wanting Luo ,&nbsp;Dmitry M. Kharitonov ,&nbsp;Di Wang ,&nbsp;Changjun Han ,&nbsp;Yongqiang Yang ,&nbsp;Vasily V. Tikhomirov","doi":"10.1016/j.physd.2025.134668","DOIUrl":"10.1016/j.physd.2025.134668","url":null,"abstract":"<div><div>Multi-color optical solitons have numerous potential applications encouraging researchers to find them by using various approaches based on both exact methods or approximate ones. Among them is widely used a variational approach, whose complexity grows fast with increasing a number of interacting waves. Therefore, a simplification of a mathematical model, describing the multi-waves interaction, without losing the key physical factors of a process under consideration is actual problem. In current paper, such simplification based on combined multi-scale-variational approach is suggested and we demonstrate its applicability for finding temporal three-color optical solitons with equidistant frequencies propagating in a medium with quadratic nonlinear response under large phase mismatching between fundamental wave and its second harmonic. At first, multi-scale method is applied to simplify original set of nonlinear Schrödinger equations. Then, a variational method is used to find approximate soliton-like solutions of the simplified equations. The solution stability criterion is derived based on the Hamiltonian of simplified equations. Computer simulation based on original set of nonlinear Schrödinger equations demonstrates the three-wave structure stabilization after short propagation distance: the pulses propagate without essential energy exchange and changing shapes i.e. some small changes occur). The three-color soliton is even robust to an influence of group velocity mismatching between interacting waves.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134668"},"PeriodicalIF":2.7,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143877469","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}