Physica D: Nonlinear Phenomena最新文献

{"title":"Soliton interaction and nonlinear localized waves in one-dimensional nonlinear acoustic metamaterials","authors":"Souleymanou Abbagari ,&nbsp;Alphonse Houwe ,&nbsp;Lanre Akinyemi ,&nbsp;Serge Yamigno Doka","doi":"10.1016/j.physd.2025.134591","DOIUrl":"10.1016/j.physd.2025.134591","url":null,"abstract":"<div><div>In this study, we investigate soliton interactions and localized wave phenomena in nonlinear acoustic metamaterials with coupling coefficients. By employing the Lindstedt-Poincaré perturbation method and a multi-scale analysis, we derive the dispersion relation for the nonlinear Schrödinger equation. The dispersion curve reveals two propagation modes: the acoustic mode and the optical mode. Particular emphasis is placed on the dynamics of bright solitons in both low- and high-frequency bands, as well as energy propagation within the forbidden bandgap. Notably, soliton pairs emerge in the allowed phonon bands, illustrating their interaction characteristics. In the forbidden bandgap, we demonstrate that when the driving amplitude exceeds the supratransmission threshold, a train of pulses forms, leading to the generation of a dark soliton. These findings are supported by full numerical simulations of the nonlinear discrete coupled diatomic chain model. Furthermore, the modified model introduces novel features, making it a promising framework for exploring delocalized wave phenomena in future study.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134591"},"PeriodicalIF":2.7,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143609969","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":"Phase synchronisation in coupled oscillator chains with endpoint heterogeneity","authors":"Daniel Galvis ,&nbsp;Nicolás Verschueren van Rees ,&nbsp;Kyle C.A. Wedgwood","doi":"10.1016/j.physd.2025.134610","DOIUrl":"10.1016/j.physd.2025.134610","url":null,"abstract":"<div><div>The emergence of collective dynamics within heterogeneous networks is a key feature of many biological networks. Heterogeneity of excitability, for example, has become a focus in the study of how pancreatic islets coordinate insulin secretion. This has raised the question of how highly excitable nodes might coordinate collective dynamics through networks where a large percentage of the population is intrinsically quiescent. To study this, we consider a discrete version of the Complex Ginzburg–Landau equation, parameterised such that in the absence of coupling, the endpoints exhibit globally attracting limit cycle behaviour and the interior nodes exhibit globally attracting trivial fixed point dynamics. Through model simulation and numerical continuation, we interrogate the relationship between model parameters and the stability of several phase-locked solutions of the system, focussing on two key solution types, the <em>chevron</em> and <em>anti-phase chevron</em> solutions, in which the exterior nodes exhibit a phase difference of 0 and <span><math><mi>π</mi></math></span>, respectively. We find that the anti-phase chevron solution stabilises as the excitability of the interior nodes decreases, or as the shearing effect of non-zero, coupling-induced amplitude perturbations from the natural limit cycle increases. Moreover, we find multiple regions of bistability with solutions with different phase synchronisation properties, highlighting that solutions observed in such networks may depend sensitively on initial conditions. Overall, our work highlights that chains with distributed heterogeneity exhibit a multitude of phase synchronised solutions, which are likely to be relevant in a range of real world networks.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134610"},"PeriodicalIF":2.7,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143610034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Construction and analysis of multi-lump solutions of dispersive long wave equations via integer partitions","authors":"Yong-Ning An,&nbsp;Rui Guo,&nbsp;Xiao-Xing Niu","doi":"10.1016/j.physd.2025.134602","DOIUrl":"10.1016/j.physd.2025.134602","url":null,"abstract":"<div><div>In this paper, the relation between the integer partition theory and a kind of rational solution of the dispersion long wave equations is studied. For the integer partition <span><math><mrow><mi>λ</mi><mo>=</mo><mfenced><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></mfenced></mrow></math></span> of positive integer <span><math><mi>N</mi></math></span>, with the degree vector <span><math><mrow><mi>m</mi><mo>=</mo><mfenced><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></mfenced></mrow></math></span>, the corresponding <span><math><mi>M</mi></math></span> lump solution can be obtained where <span><math><mrow><mi>M</mi><mo>=</mo><mi>N</mi><mo>+</mo><mi>n</mi><msub><mrow><mi>m</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>. Combined with the generalized Schur polynomial and heat polynomial, the asymptotic positions of peaks are studied, and the arrangement of multi-peak groups in multi-lump solutions are obtained, as well as the relationship between the patterns formed by single-peak groups and the corresponding integer partition.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134602"},"PeriodicalIF":2.7,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592755","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":"Robustness analysis of externally driven damped solitons in the presence of uncertainties and disorders","authors":"A. Barbosa,&nbsp;N. Kacem,&nbsp;N. Bouhaddi","doi":"10.1016/j.physd.2025.134612","DOIUrl":"10.1016/j.physd.2025.134612","url":null,"abstract":"<div><div>This paper investigates the sensitivity of localized vibrations phenomena in externally driven Duffing oscillator chains. Such investigation is conducted by generalizing the Nonlinear Schrödinger Equation (NLSE) to accommodate disorder functions in all physical parameters, beyond impurities commonly found in the literature, limited to the natural frequency of the components. Given the absence of closed-form solutions for externally driven damped systems, we employ a numerical method, followed by statistical analysis, to elucidate the effects of parameter uncertainties across the lattice on solitons behavior. Our findings highlight the diverse effects of the physical nature of uncertainties within the mechanical structure, offering insights into possible experimental investigations. Additionally, we illustrate how specific impurities along the chain, capable to nucleate oscillations, mitigate resonant chaotic behaviors, reinforcing soliton stability. The results affirm the feasibility of generating standing waves in nonlinear lattices, emphasizing their relevance beyond traditional periodic assumptions, where uncertainties in physical parameters are commonly disregarded.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134612"},"PeriodicalIF":2.7,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579633","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":"Effect of dispersal-induced death in predator–prey metapopulation system with bistable local dynamics","authors":"Sounov Marick,&nbsp;Nandadulal Bairagi","doi":"10.1016/j.physd.2025.134597","DOIUrl":"10.1016/j.physd.2025.134597","url":null,"abstract":"<div><div>Metapopulation survivability largely depends on the efficient spatial movement of dispersing populations. This study investigates the predator–prey metapopulation model, where the patches are connected by weighted mean-field coupling, capturing species loss due to inefficient dispersal, along with bistability in the local system. Using a semi-analytical approach, it dissects the dynamics of individual patch system (IPS) and homogeneous patch system (HPS), a limiting case of the metapopulation with a homogeneous population distribution. Though HPS can capture a holistic metapopulation dynamic, including persistence and extinction, it fails to differentiate multi-clustered states arising from low dispersal rates and the initial value-dependent behaviours. Our simulation results uncover various emergent metapopulation dynamics, like homogeneous steady states (HSS), global synchrony, multi-cluster and chimera states. It shows that the metapopulation exhibits amplitude death (AD) and oscillation death (OD) based on the dispersal rate, efficiency, and initial active/inactive patch numbers. Moreover, the study formulates a distance-dependent dispersal efficiency on a geometrically generated network with asymmetric patch arrangement. Distance-dependent dispersal efficiency increases the occurrence of the OD state in the parametric plane. Understanding these dynamics sheds light on species survivability in metapopulation and underscores the importance of efficient spatial movement.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134597"},"PeriodicalIF":2.7,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592754","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":"Limit cycles bifurcating from periodic integral manifold in non-smooth differential systems","authors":"Oscar A.R. Cespedes ,&nbsp;Douglas D. Novaes","doi":"10.1016/j.physd.2025.134600","DOIUrl":"10.1016/j.physd.2025.134600","url":null,"abstract":"<div><div>This paper addresses the perturbation of higher-dimensional non-smooth autonomous differential systems characterized by two zones separated by a codimension-one manifold, with an integral manifold foliated by crossing periodic solutions. Our primary focus is on developing the Melnikov method to analyze the emergence of limit cycles originating from the periodic integral manifold. While previous studies have explored the Melnikov method for autonomous perturbations of non-smooth differential systems with a linear switching manifold and with a periodic integral manifold, either open or of codimension 1, our work extends to non-smooth differential systems with a non-linear switching manifold and more general periodic integral manifolds, where the persistence of periodic orbits is of interest. We illustrate our findings through several examples, highlighting the applicability and significance of our main result.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134600"},"PeriodicalIF":2.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143561374","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":"Vegetation pattern formation and transition in dryland ecosystems with finite soil resources and inertia","authors":"Giancarlo Consolo ,&nbsp;Carmela Curró ,&nbsp;Gabriele Grifó ,&nbsp;Giovanna Valenti","doi":"10.1016/j.physd.2025.134601","DOIUrl":"10.1016/j.physd.2025.134601","url":null,"abstract":"<div><div>The formation of vegetation patterns in dryland ecosystems and the transition between different morphologies are here investigated by means of a bidimensional hyperbolic reaction-transport model. The proposed conceptual framework represents an extension of the classical Klausmeier model in which the finite carrying capacity of the soil and the inertia of biomass and water are also taken into account. The main aim of this work is to elucidate how pattern dynamics occurring at, near and far from the instability threshold are affected by the combined action of limited soil resources, inertia and climate change. To achieve this goal, a threefold investigation is carried out. First, linear stability analysis is addressed to deduce the main pattern features associated with Turing patterns at the onset of instability. Then, multiple-scale weakly nonlinear analysis is employed to characterize the pattern amplitude close to onset. In particular, the study encompasses the description of different pattern morphologies which emerge when the excited eigenmode exhibits single or double multiplicity. Finally, the transition between different patterned states is investigated in far-from-equilibrium conditions, especially to emphasize the nontrivial role played by inertia in the ecosystem response. Numerical simulations are also used to corroborate analytical predictions and to shed light on some key aspects of vegetation pattern dynamics in the context of dryland ecology.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134601"},"PeriodicalIF":2.7,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143561375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An experimental observation of intermittent extreme events in boundary layer transition","authors":"G. Balamurugan ,&nbsp;S.S. Gopalakrishnan ,&nbsp;A.C. Mandal","doi":"10.1016/j.physd.2025.134598","DOIUrl":"10.1016/j.physd.2025.134598","url":null,"abstract":"<div><div>One of the fundamental characteristics of an extreme event, which has been widely studied in diverse branches of physics, is the non-Gaussian nature of the probability distribution function. Specifically events which have amplitudes that are twice the significant wave height, which is a measure of the background state, are characterized as extreme events. Here we find a parallel of this event during the laminar–turbulent transition in a flat-plate boundary layer subjected to freestream turbulence. During the transition process spontaneous intermittent turbulent fluctuations are observed with amplitudes twice the significant wave height of the background state. The probability distribution function of events during the transition process is quantified using hotwire anemometry revealing a long-tail non-Gaussian nature as a whole, which is a fundamental characteristic of extreme events. The spatial structure of extreme fluctuation shows that they are large amplitude spatially localized structures which were obtained from simultaneous measurements made using hot-wire and time-resolved particle image velocimetry techniques. The probability of occurrence of such high intensity spatially localized turbulent fluctuations increases with the freestream velocity. Though the phenomenon of intermittency during boundary layer transition has been extensively studied, the objective of the present work is to establish its similarities to extreme events predicted in other fields of physics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134598"},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592756","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":"Periodic orbits and integrability of Rocard’s system","authors":"Xinhao Hu,&nbsp;Yilei Tang","doi":"10.1016/j.physd.2025.134594","DOIUrl":"10.1016/j.physd.2025.134594","url":null,"abstract":"<div><div>In 1941, based on Van der Pol’s relaxation oscillator equation, physicist Yves Rocard in the book (Rocard 1941) proposed a relaxation econometric oscillator to describe cyclical oscillations in the economy. Furthermore, it was later found that the model exhibits chaotic phenomenon. Rocard’s chaotic system predates Lorenz’s discovery by 22 years, which is a three-dimensional autonomous differential system. In this paper, we research periodic orbits and integrability of Rocard’s system. We study the zero-Hopf bifurcation near equilibria and center problem on center manifolds, proving that one or three periodic orbits can bifurcate through the application of the averaging method up to arbitrary finite order, while obtaining center conditions for all equilibria through Lyapunov method. Furthermore, we investigate the integrability of Rocard’s system, which has no algebraic first integrals, Darboux polynomials, or Darboux first integrals, and is not Liouvillian integrable.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"475 ","pages":"Article 134594"},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143549612","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":"How to quantify interaction strengths? A critical rethinking of the interaction Jacobian and evaluation methods for non-parametric inference in time series analysis","authors":"Takeshi Miki ,&nbsp;Chun-Wei Chang ,&nbsp;Po-Ju Ke ,&nbsp;Arndt Telschow ,&nbsp;Cheng-Han Tsai ,&nbsp;Masayuki Ushio ,&nbsp;Chih-hao Hsieh","doi":"10.1016/j.physd.2025.134613","DOIUrl":"10.1016/j.physd.2025.134613","url":null,"abstract":"<div><div>Quantifying interaction strengths between state variables in dynamical systems is essential for understanding ecological networks. Within the empirical dynamic modeling approach, multivariate S-map infers the interaction Jacobian from multivariate time series data without assuming specific dynamical models. This approach enables the non-parametric statistical inference of interspecific interactions through state space reconstruction. However, deviations in the biological interpretation and numerical implementation of the interaction Jacobian from its unique mathematical definition pose challenges. We mathematically reintroduce the interaction Jacobian by starting our derivation with differential quotients, uncovering two key problems: (1) the mismatch between the interaction Jacobian and its biological meaning complicates comparisons between interspecific and intraspecific interaction strengths; (2) the interaction Jacobian is not fully implemented in the parametric Jacobian numerically derived from given parametric models, especially ordinary differential equation models. As a result, model-based evaluations of S-map methods become inappropriate. To address these problems, (1) we propose adjusting the diagonal elements of the interaction Jacobian by subtracting 1 to resolve the comparability problem between interspecific and intraspecific interaction strengths. Simulations of population dynamics showed that this adjustment prevents overestimation of intraspecific interaction strengths, allowing for meaningful comparisons. (2) We introduce an alternative parametric Jacobian and then cumulative interaction strength (CIS), providing a more rigorous benchmark for evaluating S-map methods. Furthermore, we demonstrated that the numerical gap between CIS and the existing parametric Jacobian is substantial in realistic scenarios, suggesting CIS as a preferred benchmark for future evaluations. These solutions offer a clearer framework for developing non-parametric approaches in ecological time series analysis.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134613"},"PeriodicalIF":2.7,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629411","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}