Physica D: Nonlinear Phenomena最新文献

{"title":"Decadal variability of the Antarctic Circumpolar Current in an idealized chaotic ocean–atmosphere coupled model","authors":"Florian Sévellec","doi":"10.1016/j.physd.2025.134888","DOIUrl":"10.1016/j.physd.2025.134888","url":null,"abstract":"<div><div>An idealized ocean–atmosphere coupled model exhibiting chaotic behaviour is developed to represent the dynamics of the Antarctic Circumpolar Current, one of the most intense ocean currents on Earth. On a meridional-depth plane, the model is driven by the competition between eddy-induced advection and wind-induced advection, where a feedback of meridional ocean temperature contrast on the wind intensity is allowed. Along the zonal direction, the lattice of individual meridional-depth dynamics are zonally coupled through zonal turbulent diffusivity. We show that ocean–atmosphere coupling is crucial to set the chaotic dynamics, whereas the zonal turbulent diffusivity is crucial for setting a realistic intensity of the Antarctic Circumpolar Current. For a value of zonal turbulent diffusivity between 200 and 10<!--> <!-->000 m<span><math><msup><mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span> s⁻¹ the zonal mean transport is 121 Sv (1 Sv <span><math><mrow><mo>≡</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>6</mn></mrow></msup></mrow></math></span> m<span><math><msup><mrow></mrow><mrow><mn>3</mn></mrow></msup></math></span> s⁻¹) and exhibits a main spectral signature at 8.1 years. The diffusivity coefficient controls the level of zonal synchronicity of the Antarctic Circumpolar Current going from a fully zonally-independent system to a fully synchronized lattice with no zonal variation. The realistic regime corresponds to an intermediate level of synchronicity, where the footprint length scale measured the zonal distance over which local meridional-depth dynamics are impacting each other. This zonal length scale footprint is set by the competition between the zonal turbulent diffusivity, zonally coupling the dynamics, and the extreme event (<span><math><mo>&gt;</mo></math></span>82 percentile) return period (<span><math><mo>∼</mo></math></span>48.5 years), resetting the local meridional-depth dynamics.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134888"},"PeriodicalIF":2.9,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932780","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":"Highly-sensitive measure of complexity captures Boolean networks’ regimes and temporal order more optimally","authors":"Manuel de J. Luevano-Robledo,&nbsp;Alejandro Puga-Candelas","doi":"10.1016/j.physd.2025.134844","DOIUrl":"10.1016/j.physd.2025.134844","url":null,"abstract":"<div><div>In this work, several random Boolean networks (RBNs) are generated and analyzed based on two fundamental features: their time evolution diagrams and their transition diagrams. For this purpose, we estimate randomness using three measures, among which Algorithmic Complexity stands out because it can (a) reveal transitions towards the chaotic regime more distinctly, and (b) disclose the algorithmic contribution of certain states to the transition diagrams, including their relationship with the order they occupy in the temporal evolution of the respective RBN. Results from both types of analysis illustrate the potential of Algorithmic Complexity and Perturbation Analysis for Boolean networks, paving the way for possible applications in modeling biological regulatory networks.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134844"},"PeriodicalIF":2.9,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893203","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 detached-eddy simulation methodology for interfacial mixing flows","authors":"Hansong Xie ,&nbsp;Mengjuan Xiao ,&nbsp;Yaomin Zhao ,&nbsp;Yousheng Zhang ,&nbsp;Jianchun Wang ,&nbsp;Yipeng Shi","doi":"10.1016/j.physd.2025.134892","DOIUrl":"10.1016/j.physd.2025.134892","url":null,"abstract":"<div><div>This study focuses on modeling the three-dimensional (3D) mixing flows induced by hydrodynamics interfacial instabilities, specifically, Rayleigh–Taylor (RT), Richtmyer–Meshkov (RM), and Kelvin–Helmholtz instabilities. These flows arise from irregular multimode perturbations, undergoing mixing transition, and eventually develop into turbulence. Such evolution processes are ubiquitous in both natural phenomena (e.g., supernova explosions) and engineering applications (e.g., inertial confinement fusion), and in these practical scenarios, flows are generally compressible. Efficient simulations of this entire flow evolution hold significant value, yet existing approaches face major challenges. Conventional Reynolds-averaged Navier–Stokes (RANS) methods, while computationally efficient, often employ reduced-dimensional approximations, thereby failing to resolve the spectrum of initial perturbations and the dynamics of 3D coherent structures. Conversely, direct numerical simulation and large eddy simulation (LES), though more accurate, remain computationally intractable for practical problems in the foreseeable future. To address that, this study explores a hybrid LES/RANS framework designed to efficiently simulate 3D mixing flows across all evolutionary stages at a fraction of the computational cost of pure LES. This approach leverages key physical insights: small-scale structures dominate the core mixing region, where RANS is computationally optimal, while large-scale bubbles and spikes prevail at the mixing front, where LES excels in resolving coherent vortical structures. By extending the detached-eddy simulation methodology — originally developed for boundary layers and separated flows — to interfacial mixing problems, we achieve an automatic transition between RANS and LES models in mixing regions. Specifically, the <span><math><mi>K</mi></math></span>-<span><math><mi>L</mi></math></span> turbulence model serves as the foundation, with its turbulent dissipation term’s length scale reformulated into a blended expression regarding RANS length scale and grid spacing. The bridged function is innovatively constructed based on the local mixing degree represented as <span><math><mrow><mn>4</mn><msub><mrow><mi>Y</mi></mrow><mrow><mi>β</mi></mrow></msub><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>, to dynamically partition the mixing domain, here <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>β</mi></mrow></msub></math></span> denoting mass fraction of fluid <span><math><mi>β</mi></math></span>. It enables the single model to operate as the standard <span><math><mi>K</mi></math></span>-<span><math><mi>L</mi></math></span> RANS model in the core region while functioning as the one-equation LES model near the mixing front. Validations by several typical cases, involving the planar reshocked RM mixing, inverse-chevron reshocked RM mixing with noteworthy tra","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134892"},"PeriodicalIF":2.9,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896258","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":"Dynamics of 1D discontinuous maps with multiple partitions and linear functions having the same fixed point. An application to financial market modeling","authors":"Laura Gardini ,&nbsp;Davide Radi ,&nbsp;Noemi Schmitt ,&nbsp;Iryna Sushko ,&nbsp;Frank Westerhoff","doi":"10.1016/j.physd.2025.134895","DOIUrl":"10.1016/j.physd.2025.134895","url":null,"abstract":"<div><div>Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a finite number of partitions and functions sharing the same real fixed point. We show that the dynamics of this class of maps can be analyzed using the well-known piecewise linear circle map. We prove that their bounded behavior, when unrelated to the fixed point, may consist of either nonhyperbolic cycles or quasiperiodic orbits densely filling certain segments, with possible coexistence. A corresponding model describing the price dynamics of a financial market serves as an illustrative example. While simulated model dynamics may be mistaken for chaotic behavior, our results demonstrate that they are quasiperiodic.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134895"},"PeriodicalIF":2.9,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902620","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":"Blurring the Busse balloon: Patterns in a stochastic Klausmeier model","authors":"Christian H.S. Hamster ,&nbsp;Peter van Heijster ,&nbsp;Eric Siero","doi":"10.1016/j.physd.2025.134863","DOIUrl":"10.1016/j.physd.2025.134863","url":null,"abstract":"<div><div>We investigate the effect of stochastic forcing on spatially periodic patterns in a one-dimensional Klausmeier model for dryland vegetation. Using numerical methods, we can accurately describe the transient dynamics of the stochastic solutions and compare several notions of stability. In particular, we show that the boundary of the Busse balloon — which represents the deterministically stable patterns — becomes blurred under the stochastic perturbations and that the stochastic stability heavily depends on the model parameters, the intensity of the noise and the location of the wave number of the periodic pattern within the deterministic Busse balloon.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134863"},"PeriodicalIF":2.9,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887065","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":"Classification and dynamic analysis of nonlinear wave structures evolving from initial discontinuities in the coupled Zakharov–Ito system","authors":"Fan Wu ,&nbsp;Yaqing Liu ,&nbsp;Zhenya Yan","doi":"10.1016/j.physd.2025.134896","DOIUrl":"10.1016/j.physd.2025.134896","url":null,"abstract":"<div><div>In this paper, we investigate into the possible wave pattern solutions for the Riemann problem associated with the Zakharov–Ito equation, utilizing the Whitham modulation theory. Using the finite-gap integration technique, we derive the zero-phase and single-phase periodic solutions pertinent to the Whitham equations. By incorporating the self-similar variable, we develop the fundamental structures of rarefaction waves and dispersive shock waves. It is observed that the dispersionless equation admits a solution through the integration of hodograph transformation and Fourier transform methodologies. A comprehensive classification of the possible wave structures of the Zakharov–Ito equation is presented for all conceivable jump conditions at the initial discontinuity, yielding combinations of plateaus, rarefaction waves, and dispersive shock waves.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134896"},"PeriodicalIF":2.9,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896257","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 the Selkov systems","authors":"Chen Cao ,&nbsp;Hebai Chen ,&nbsp;Jaume Llibre ,&nbsp;Yilei Tang","doi":"10.1016/j.physd.2025.134894","DOIUrl":"10.1016/j.physd.2025.134894","url":null,"abstract":"<div><div>The aim of this paper is to investigate the problem of limit cycles and global dynamics for the general case of the Selkov system. By applying limit cycle theory for Liénard systems, we first transform the Selkov systems into Liénard systems. Then the theory and techniques related to limit cycles for Liénard systems can be utilized and further developed. We obtain a new criterion for the uniqueness of limit cycles in general Liénard systems. Consequently, we address the majority of parameter cases for the conjecture regarding the uniqueness of limit cycles proposed in the literature. Finally, we present the global bifurcations and dynamical structures of the system in the Poincaré disc.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134894"},"PeriodicalIF":2.9,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887064","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":"Geometric analysis of Rotation-Benjamin–Bona–Mahony and Rotation-Korteweg–de Vries equations with dissipative perturbations","authors":"Shuting Chen ,&nbsp;Zengji Du","doi":"10.1016/j.physd.2025.134881","DOIUrl":"10.1016/j.physd.2025.134881","url":null,"abstract":"<div><div>In this paper, we focus on the dynamics of the Rotation-Benjamin–Bona–Mahony equation and the Rotation-Korteweg–de Vries equation with dissipative perturbations. These mathematical models can be used to describe shallow-water wave propagation in equatorial ocean regions, considering the weak Coriolis effect due to Earth’s rotation. By applying geometric singular perturbation methods and invariant manifold theory, we establish the existence of solitary waves and periodic waves in the presence and absence of Marangoni effects. Moreover, the wave speed monotonicity is derived by analyzing the ratios of Abelian integrals. Finally, we provide the upper and lower bounds and monotonicity of the period for traveling wave solutions as the small positive parameter vanishes and illustrate the asymptotic properties of solutions by using the asymptotic theory.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134881"},"PeriodicalIF":2.9,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144879378","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":"Quasisteady patterns in interfaces: Folding and faceting","authors":"Vinh Nguyen ,&nbsp;Keith Promislow ,&nbsp;Brian Wetton","doi":"10.1016/j.physd.2025.134861","DOIUrl":"10.1016/j.physd.2025.134861","url":null,"abstract":"<div><div>We present a systematic derivation of the gradient flows associated to a broad class of interfacial energies, emphasizing the relation between intrinsic and extrinsic variations of the interface. We show that the intrinsic variables formulation brings the gradient flow into alignment with the traditional analysis of quasi-steady dynamical systems defined on a stationary domain. Gradient flows are derived for model systems which exhibit quasi-steady pattern formation including coarsening among faceted interfaces and nonlocal interactions that model membrane self-adhesion and self-avoidance.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134861"},"PeriodicalIF":2.9,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144890852","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":"Nonlinear dynamics of periodic solutions in electrostatic MEMS: Theory and numerical bifurcation analysis","authors":"Zhibo Cheng ,&nbsp;Ci Kong ,&nbsp;Qigang Yuan","doi":"10.1016/j.physd.2025.134887","DOIUrl":"10.1016/j.physd.2025.134887","url":null,"abstract":"<div><div>MEMS dynamics are critical in determining the performance, reliability and functionality of microdevices in diverse technological applications. In this paper, we study the bifurcations and dynamics of periodic solutions to a singular differential equation that models an electrostatically actuated MEMS with nonlinear squeeze film damping effect. Applying the method of upper and lower functions and Leray–Schauder degree, we obtain an Ambrosetti–Prodi type result of periodic solutions and analyze their dynamics as the parameter tend to infinity. The results provide some new insights into the open problem concerning saddle–node bifurcation in MEMS dynamics proposed by P. J. Torres. Using numerical bifurcation analysis, we provide the bifurcation diagrams to visualize the main theorems and reveal the equation’s rich dynamic behaviors including saddle–node and period-doubling bifurcations of periodic solutions. A novel pattern of multiplicity in periodic solutions generated by bifurcations is observed: as the parameters vary, the equation transitions from two coexisting <span><math><mi>T</mi></math></span>-periodic solutions to four, and then to six, including four <span><math><mi>T</mi></math></span>-periodic solutions and two <span><math><mrow><mn>2</mn><mi>T</mi></mrow></math></span>-periodic solutions.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"482 ","pages":"Article 134887"},"PeriodicalIF":2.9,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887061","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}