Physica D: Nonlinear Phenomena最新文献

{"title":"Stabilising millennial oscillations in large-scale ocean circulation with a delayed feedback due to a circumpolar current","authors":"Andrew Keane ,&nbsp;Alexandre Pohl ,&nbsp;Henk A. Dijkstra ,&nbsp;Andy Ridgwell","doi":"10.1016/j.physd.2025.134680","DOIUrl":"10.1016/j.physd.2025.134680","url":null,"abstract":"<div><div>The global ocean circulation plays a pivotal role in the regulation of the Earth’s climate. The specific pattern and strength of circulation also determines how carbon and nutrients are cycled and via the resulting distribution of dissolved oxygen, where habitats suitable for marine animals occur. However, evidence from both geological data and models suggests that state transitions in circulation patterns have occurred in the past. Understanding the controls on marine environmental conditions and biodiversity requires a full appreciation of the nature and drivers of such transitions. Here we present stable millennial oscillations of meridional overturning circulation in an Earth system model of intermediate complexity, cGENIE, that appear to only occur in the presence of a circumpolar current. To demonstrate that a circumpolar current can act as a driver of stable oscillations, we adapt a simple ocean box model to include a delayed feedback to represent the effect of a circumpolar current on meridional overturning circulation. We investigate the millennial oscillatory solutions that arise in the box model by bifurcation analysis and show that the model can reproduce the same bifurcation structure observed in the Earth system model. Our results provide new insights into the nature of oscillations that could have occurred under certain continental configurations in the geological past, and also highlight the potential influence of the changing Antarctic circumpolar current speed on the stability of the Atlantic meridional overturning circulation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134680"},"PeriodicalIF":2.7,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143878947","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":"Indicator functions detect tangentially transient behaviour on decaying normally hyperbolic invariant manifolds","authors":"Francisco Gonzalez Montoya ,&nbsp;Christof Jung","doi":"10.1016/j.physd.2025.134686","DOIUrl":"10.1016/j.physd.2025.134686","url":null,"abstract":"<div><div>We study the decay scenario of a codimension-2 NHIM in a three-degrees-of-freedom Hamiltonian system under increasing perturbation when the NHIM loses its normal hyperbolicity. On one hand, we follow this decay in the Poincaré map for the internal dynamics of the NHIM. On the other hand, we also follow the decay in a time delay function calculated on a 2-dimensional plane in the phase space of the system. In addition, we observe the role of tangential transient effects on the decaying NHIM and their manifestation in the delay time indicator function. We obtain ideas on how the decay of NHIMs and the tangential transient effects are encoded in indicator functions. As an example of demonstration, we use the motion of an electron in a perturbed magnetic dipole field.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134686"},"PeriodicalIF":2.7,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868002","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":"Complete synchronization and topology identification of a time-varying network group constituted of chaotic single-ring erbium-doped fiber lasers","authors":"Chengren Li ,&nbsp;Zhen Zhang ,&nbsp;Jianmin Wang ,&nbsp;Li Cui ,&nbsp;Wei Hu ,&nbsp;Chunlai Guo","doi":"10.1016/j.physd.2025.134695","DOIUrl":"10.1016/j.physd.2025.134695","url":null,"abstract":"<div><div>A universal and efficient strategy is proposed in this work to simultaneously realize the complete synchronization and topology identification of a time-varying network group consisting of chaotic single-ring erbium-doped fiber lasers (SREDFLs). The synchronization controller and identification laws of uncertain inner and outer coupling matrix elements are optimally designed based on the Lyapunov stability theorem. To verify the effectiveness of the proposed technique, sixteen SREDFLs are selected as the nodes to construct a time-varying network group, including four subnetworks, and there exist four nodes within each subnetwork. The simulation results show that the complete synchronization between the response and drive network groups has been achieved, and at the same time, all the undetermined inner and outer coupling matrix elements of the network group can also be accurately and quickly identified even though the topology of the complex network changes with time, indicating that both the synchronization controller and the identification laws designed in our work are feasible and efficient.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134695"},"PeriodicalIF":2.7,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143882269","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":"Solutions of an extended Duffing–van der Pol equation with variable coefficients","authors":"O. Cornejo-Pérez ,&nbsp;P. Albares ,&nbsp;J. Negro","doi":"10.1016/j.physd.2025.134675","DOIUrl":"10.1016/j.physd.2025.134675","url":null,"abstract":"<div><div>In this work, exact solutions of the nonlinear cubic–quintic Duffing–van der Pol oscillator with variable coefficients are obtained. Two approaches have been applied, one based on the factorization method combined with the Field Method, and a second one relying on Painlevé analysis. Both procedures allow us to find the same exact solutions to the problem. The Lagrangian formalism for this system is also derived. Moreover, some examples for particular choices of the time-dependent coefficients, and their corresponding general and particular exact solutions are presented.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134675"},"PeriodicalIF":2.7,"publicationDate":"2025-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143898469","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":"Four-fifths laws in incompressible and magnetized fluids: Helicity, energy and cross-helicity","authors":"Yulin Ye ,&nbsp;Yanqing Wang ,&nbsp;Otto Chkhetiani","doi":"10.1016/j.physd.2025.134655","DOIUrl":"10.1016/j.physd.2025.134655","url":null,"abstract":"<div><div>In this paper, we are concerned with the Kolmogorov’s scaling laws of conserved quantities in incompressible fluids. By means of Eyink’s longitudinal structure functions and the analysis of interaction of different physical quantities, we extend celebrated four-fifths laws from energy to helicity in incompressible fluid and, total energy and cross-helicity in magnetohydrodynamic flow. In contrast to pervious 4/5 laws of energy and cross-helicity in magnetized fluids obtained by Politano and Pouquet, they are in terms of the mixed third-order structure functions rather than the structure coupling correlation functions. New insights to the cascade rate of inviscid invariants are provided in incompressible turbulence.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134655"},"PeriodicalIF":2.7,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143859140","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":"Kernel methods for the approximation of the eigenfunctions of the Koopman operator","authors":"Jonghyeon Lee ,&nbsp;Boumediene Hamzi ,&nbsp;Boya Hou ,&nbsp;Houman Owhadi ,&nbsp;Gabriele Santin ,&nbsp;Umesh Vaidya","doi":"10.1016/j.physd.2025.134662","DOIUrl":"10.1016/j.physd.2025.134662","url":null,"abstract":"<div><div>The Koopman operator provides a linear framework to study nonlinear dynamical systems. Its spectra offer valuable insights into system dynamics, but the operator can exhibit both discrete and continuous spectra, complicating direct computations. In this paper, we introduce a kernel-based method to construct the principal eigenfunctions of the Koopman operator without explicitly computing the operator itself. These principal eigenfunctions are associated with the equilibrium dynamics, and their eigenvalues match those of the linearization of the nonlinear system at the equilibrium point. We exploit the structure of the principal eigenfunctions by decomposing them into linear and nonlinear components. The linear part corresponds to the left eigenvector of the system’s linearization at the equilibrium, while the nonlinear part is obtained by solving a partial differential equation (PDE) using kernel methods. Our approach avoids common issues such as spectral pollution and spurious eigenvalues, which can arise in previous methods. We demonstrate the effectiveness of our algorithm through numerical examples.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134662"},"PeriodicalIF":2.7,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143848264","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":"All meromorphic solutions of a 3D Lotka–Volterra system: Detecting partial integrability","authors":"Techheang Meng,&nbsp;Rod Halburd","doi":"10.1016/j.physd.2025.134674","DOIUrl":"10.1016/j.physd.2025.134674","url":null,"abstract":"<div><div>For an autonomous system of ordinary differential equations, the existence of a meromorphic general solution is equivalent to the Painlevé property, which is widely used to detect integrability. We find all meromorphic solutions of a multi-parameter three-dimensional Lotka–Volterra system. Some cases correspond to particular choices of the parameters for which only some solutions are meromorphic, while the general solution is branched. The main difficulty is to prove that all meromorphic solutions have been found. The proof relies on a detailed study of local series expansions combined with value distribution results from Nevanlinna theory.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134674"},"PeriodicalIF":2.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868003","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 the higher-order-rogue-wave signals due to a coupled Noguchi electrical transmission line","authors":"Gabriel Djelah ,&nbsp;Saidou Abdoulkary ,&nbsp;Fabien II Ndzana ,&nbsp;Alidou Mohamadou","doi":"10.1016/j.physd.2025.134660","DOIUrl":"10.1016/j.physd.2025.134660","url":null,"abstract":"<div><div>We are theoretically and numerically studying the behavior of a transversely coupled Noguchi electric transmission line with a series connection of linear inductor and capacitor. Using the reductive perturbation method in the semi-discrete limit, we derive a 2D-cubic-quintic nonlinear Schrödinger equation governing the behavior of the system. Performing the generalized Darboux transformation we find higher-order rogue waves including first-, second- and third-one as solutions. Moreover, analytic predictions through Modulational Instability analysis show that the lattice can support a variety of pairs of solitons including envelope-envelope, envelope-hole, hole-envelope and hole–hole. Both rogue waves and soliton can propagate in forward or backward direction according to their frequencies. The study of the propagation properties of the rogue wave signals through the system shows that their width and velocity depend on the network parameters and wavenumbers as well as the real parameter responsible for the quintic effects. Finally, our results reveal that the network can adopt a dual right-handed or a composite right- and left-handed behavior.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134660"},"PeriodicalIF":2.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868004","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":"Bifurcations patterns and heat transmissions in couple-stress fluid layer with isothermal rigid boundaries","authors":"Purbasha Deb,&nbsp;G.C. Layek","doi":"10.1016/j.physd.2025.134672","DOIUrl":"10.1016/j.physd.2025.134672","url":null,"abstract":"<div><div>In this work, we investigate the dynamical patterns of thermo-convective loops in a horizontal shallow layer of couple-stress fluid confined between isothermal rigid boundaries and heated from beneath. The novelty of this study lies in examining the influences of couple-stresses on the dynamical patterns of fluid convection in the presence of rigid boundaries. Both the linear and non-linear stability analyses are performed. It is found that the critical Rayleigh number for the onset of convection increases significantly with the couple-stress parameter (<span><math><mi>C</mi></math></span>). Using low-order Galerkin approximations within the framework of non-linear stability analysis, a three-dimensional, non-linear, dissipative system governed by four control parameters is derived. Studies reveal that the transitions to the stationary and oscillatory convections (through pitchfork and Hopf bifurcations, respectively) detain with the enhancement of <span><math><mi>C</mi></math></span>, consistent with observations for free-isothermal boundaries. Notably, a striking outcome of this research is that, unlike the stress-free case, the subcritical Hopf bifurcation evolves to supercritical one as <span><math><mi>C</mi></math></span> exceeds a critical threshold of approximately 0.1022708, and it fundamentally alters the flow dynamics. At this threshold value of the parameter <span><math><mi>C</mi></math></span>, the system experiences a codimension-2 Bautin bifurcation, which is not likely to appear in the classical Lorenz system for realistic parameters values. Furthermore, the mode of heat transport stabilizes from convection to conduction with increasing <span><math><mi>C</mi></math></span>. Variations in the stream function and isotherm function with respect to <span><math><mi>C</mi></math></span> are analyzed and depicted. Additionally, the effect of couple-stresses on the chaotic regime at a high reduced normalized Rayleigh number (<span><math><mrow><msub><mrow><mi>r</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>200</mn></mrow></math></span>) exhibits intermittent behavior, and chaos is entirely suppressed for a suitable value of <span><math><mi>C</mi></math></span>, indicating the stabilization of the system.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134672"},"PeriodicalIF":2.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143839116","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":"On Euler equation for incoherent fluid in curved spaces","authors":"B.G. Konopelchenko ,&nbsp;G. Ortenzi","doi":"10.1016/j.physd.2025.134667","DOIUrl":"10.1016/j.physd.2025.134667","url":null,"abstract":"<div><div>Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated integrals allows to construct several types of hodograph equations. These hodograph equations provide us with various classes of solutions of the Euler equation, including stationary solutions. Particular cases of cone and sphere in the 3-dimensional Euclidean space are analysed in detail. Euler equation on the sphere in the 4-dimensional Euclidean space is considered too.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134667"},"PeriodicalIF":2.7,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829168","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}