Physica D: Nonlinear Phenomena最新文献_第9页

The nonlinear steepest descent approach to the long-time asymptotics of the three-coupled Lakshmanan–Porsezian–Daniel model 三耦合Lakshmanan-Porsezian-Daniel模型长期渐近性的非线性最陡下降方法

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-13 DOI: 10.1016/j.physd.2025.134713

Yi Zhao

{"title":"The nonlinear steepest descent approach to the long-time asymptotics of the three-coupled Lakshmanan–Porsezian–Daniel model","authors":"Yi Zhao","doi":"10.1016/j.physd.2025.134713","DOIUrl":"10.1016/j.physd.2025.134713","url":null,"abstract":"<div><div>In this paper, the long-time asymptotic behavior of the three-coupled Lakshmanan–Porsezian–Daniel (LPD) model with Schwartz initial data is investigated by the nonlinear steepest descent approach. Based on the Lax pair of the LPD model, a Riemann–Hilbert problem associated with the initial value problem is constructed. Further a sequence of transformations change the Riemann–Hilbert problem into a tractable form via the Deift–Zhou nonlinear steepest descent approach. Then the long-time asymptotics of the LPD model is obtained through reconstruction formula. What distinguishes the 2 × 2 spectral problem is that we treat the matrix in a block form, the advantage of which is that the matrix can be regarded as a block diagonal matrix without being strictly diagonal, necessitating the complexity of the function <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>. The primary limitation of this approach is that it does not enable direct acquisition of the solution <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>. To address this challenge, we employ a term involves <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>−</mo><mi>I</mi><mi>⋅</mi><mo>det</mo><mi>δ</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span>, then the term can be asymptotically estimated as <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>t</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>. The distinguishing feature of the long-time asymptotic analysis for our problem, when compared with the nonlinear Schrödinger equation and Hirota equation, lies in the presence of three critical points.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"478 ","pages":"Article 134713"},"PeriodicalIF":2.7,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144088783","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}

引用次数: 0

Interaction of plane solitons in the 2D Gardner equation 二维Gardner方程中平面孤子的相互作用

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-13 DOI: 10.1016/j.physd.2025.134736

R. Fariello , Y.A. Stepanyants , T.G. Talipova

引用次数: 0

Fractal characteristics of interfaces in Richtmyer–Meshkov turbulence richmyer - meshkov湍流中界面的分形特征

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-12 DOI: 10.1016/j.physd.2025.134711

Yue Zhang , Zhangbo Zhou , Wan Cheng , Juchun Ding , Xisheng Luo

{"title":"Fractal characteristics of interfaces in Richtmyer–Meshkov turbulence","authors":"Yue Zhang , Zhangbo Zhou , Wan Cheng , Juchun Ding , Xisheng Luo","doi":"10.1016/j.physd.2025.134711","DOIUrl":"10.1016/j.physd.2025.134711","url":null,"abstract":"<div><div>This work investigates the fractal dimension of the spike front and the bubble front in Richtmyer–Meshkov (RM) turbulence with initial broadband and narrowband perturbations. The fractal dimension <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>f</mi></mrow></msub></math></span> of interfaces is found to be intimately associated with interfacial mixing, exhibiting a gradual increase with interface evolution until it attains a stable value, between <span><math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>≈</mo><mn>2</mn><mo>.</mo><mn>2</mn><mo>∼</mo><mn>2</mn><mo>.</mo><mn>33</mn></mrow></math></span>, upon entering the self-similar stage. The fractal dimension on the spike front is closer to the universal fractal dimension of fully-developed turbulence, indicating stronger turbulent fluctuations there. Large-scale perturbations render the interfaces more two-dimensional thereby resulting in a lower fractal dimension. The results demonstrate that the fractal dimension, <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>f</mi><mn>3</mn></mrow></msub></math></span>, of a surface in three dimensions can be faithfully reflected by the fractal dimension, <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>f</mi><mn>2</mn></mrow></msub></math></span>, of the interface of its two-dimensional projection. This finding validates the additive rule of <span><math><mrow><msub><mrow><mi>D</mi></mrow><mrow><mi>f</mi><mn>3</mn></mrow></msub><mo>=</mo><msub><mrow><mi>D</mi></mrow><mrow><mi>f</mi><mn>2</mn></mrow></msub><mo>+</mo><mn>1</mn></mrow></math></span> in RM turbulence, which is of considerable utility for experimental research. The filtering approach is furthermore employed to illustrate the scale-invariance of the fractal interfaces. The fractal features of the early spike and bubble interfaces can be described by a simple model fractal of the Koch curve, with distinct scale factors.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134711"},"PeriodicalIF":2.7,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143947152","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}

引用次数: 0

Kernel Sum of Squares for data adapted kernel learning of dynamical systems from data: A global optimization approach 基于数据的动态系统核学习的核平方和：一种全局优化方法

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-12 DOI: 10.1016/j.physd.2025.134693

Daniel Lengyel , Boumediene Hamzi , Houman Owhadi , Panos Parpas

{"title":"Kernel Sum of Squares for data adapted kernel learning of dynamical systems from data: A global optimization approach","authors":"Daniel Lengyel , Boumediene Hamzi , Houman Owhadi , Panos Parpas","doi":"10.1016/j.physd.2025.134693","DOIUrl":"10.1016/j.physd.2025.134693","url":null,"abstract":"<div><div>This paper examines the application of the Kernel Sum of Squares (KSOS) method for enhancing kernel learning from data, particularly in the context of dynamical systems. Traditional kernel-based methods, despite their theoretical soundness and numerical efficiency, frequently struggle with selecting optimal base kernels and parameter tuning, especially with gradient-based methods prone to local optima. KSOS mitigates these issues by leveraging a global optimization framework with kernel-based surrogate functions, thereby achieving more reliable and precise learning of dynamical systems. Through comprehensive numerical experiments on the Logistic Map, Henon Map, and Lorentz System, KSOS is shown to consistently outperform gradient descent in minimizing the relative-<span><math><mi>ρ</mi></math></span> metric and improving kernel accuracy. These results highlight KSOS’s effectiveness in predicting the behavior of chaotic dynamical systems, demonstrating its capability to adapt kernels to underlying dynamics and enhance the robustness and predictive power of kernel-based approaches, making it a valuable asset for time series analysis in various scientific fields.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"478 ","pages":"Article 134693"},"PeriodicalIF":2.7,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144098858","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}

引用次数: 0

Aperiodically intermittent H∞ synchronization of coupled complex-valued neural networks with and without parameter uncertainties 有和无参数不确定性耦合复值神经网络的非周期间歇H∞同步

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-12 DOI: 10.1016/j.physd.2025.134694

Yanli Huang, Yuqing Jia

{"title":"Aperiodically intermittent H∞ synchronization of coupled complex-valued neural networks with and without parameter uncertainties","authors":"Yanli Huang, Yuqing Jia","doi":"10.1016/j.physd.2025.134694","DOIUrl":"10.1016/j.physd.2025.134694","url":null,"abstract":"<div><div>In this paper, we investigate aperiodically intermittent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> synchronization and robustly aperiodically intermittent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> synchronization for both coupled complex-valued neural networks (CCVNNs) and coupled complex-valued delayed neural networks (CCVDNNs). Initially, certain synchronization criteria for CCVNNs are established using suitable Lyapunov functionals in conjunction with a variety of inequality techniques. Furthermore, we also examine robust synchronization of CCVNNs, taking into account the impact of parameter uncertainties in neural networks. In addition, the corresponding aperiodically intermittent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> synchronization and robustly aperiodically intermittent <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> synchronization results are generalized to the network of CCVDNNs, in which the activation function is time-varying delayed. Finally, two numerical examples prove the reliability and the benefits of the proposed results.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134694"},"PeriodicalIF":2.7,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143942296","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}

引用次数: 0

Analysis of power law behavior of local cortical neurodynamics 局部皮质神经动力学的幂律行为分析

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-10 DOI: 10.1016/j.physd.2025.134733

Karolina Armonaite , Livio Conti , Marco Balsi , Luca Paulon , Franca Tecchio

{"title":"Analysis of power law behavior of local cortical neurodynamics","authors":"Karolina Armonaite , Livio Conti , Marco Balsi , Luca Paulon , Franca Tecchio","doi":"10.1016/j.physd.2025.134733","DOIUrl":"10.1016/j.physd.2025.134733","url":null,"abstract":"<div><div>Growing evidence suggests that neuronal electrical activity, the neurodynamics, contains specific signatures for distinct cortical parcels of the brain, potentially enabling cortex classification based on it, even in resting states. However, existing algorithms for extracting specific characteristics may succeed only in specific cases, or well selected groups, but often fail to identify stable features across the general populations. Our study examines intracranial stereotactic-electroencephalographic (sEEG) recordings, assessing power-law behavior in power spectral density during wakefulness and sleep stages across three gyri: precentral, postcentral and superior temporal, in 55 subjects. Results indicate the presence of a power-law behavior, implying scale-free dynamics in investigated areas. Notably, power-law exponent in high frequency range distinguishes cortical parcels both in wakefulness and sleep and suggests a stable scale-free pattern within each region possibly regardless of the state. This insight offers valuable guidance for evaluating physiological aspects of local neurodynamics and supports population-level functional cortex parceling.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134733"},"PeriodicalIF":2.7,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144089792","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}

引用次数: 0

A bound state attractor in optical turbulence 光学湍流中的束缚态吸引子

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-09 DOI: 10.1016/j.physd.2025.134687

Clément Colléaux , Jonathan Skipp , Sergey Nazarenko , Jason Laurie

{"title":"A bound state attractor in optical turbulence","authors":"Clément Colléaux , Jonathan Skipp , Sergey Nazarenko , Jason Laurie","doi":"10.1016/j.physd.2025.134687","DOIUrl":"10.1016/j.physd.2025.134687","url":null,"abstract":"<div><div>We study numerically the nonintegrable dynamics of coherent, solitonic, nonlinear waves, in a spatially nonlocal nonlinear Schrödinger equation relevant to realistic modelling of optical systems: the Schrödinger–Helmholtz equation. We observe a single oscillating, coherent solitary wave emerging from a variety of initial conditions. Using the direct scattering transform of the (integrable) cubic nonlinear Schrödinger equation, we find that this structure is a bound state, comprising of a primary and secondary soliton whose amplitudes oscillate in phase opposition. We interpret this as the solitons periodically exchanging mass. We also observe bound states comprising of three oscillating solitons, hinting at the existence of a family of multi-soliton bound states. Focusing on the two-soliton bound state, we observe it self-organising from an initial state of incoherent turbulence, and from solitonic structures launched into the system. When a single (primary) solitonic structure is launched, a resonance process between it and waves in the system generates the secondary soliton, resulting in the bound state. Further, when two solitons are initially launched, we show that they can merge if their phases are synchronised when they collide. When the system is launched from a turbulent state comprised of many initial solitons, we propose that the bound state formation is preceded by a sequence of binary collisions, in which the mass is transferred on average from the weak soliton to the strong one, with occasional soliton mergers. Both processes lead to increasingly stronger and fewer dominant solitons. The final state – a solitary bound state surrounded by weakly nonlinear waves – is robust and ubiquitous. We propose that for nonlocal media, a bound state comprising of at least two solitons is a more typical statistical attractor than the single-soliton attractor suggested in previous literature.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134687"},"PeriodicalIF":2.7,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934567","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}

引用次数: 0

Model reduction of nonlinear time-delay systems via ODE approximation and spectral submanifolds 基于ODE逼近和谱子流形的非线性时滞系统模型约简

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-09 DOI: 10.1016/j.physd.2025.134701

Yuan Tang, Mingwu Li

{"title":"Model reduction of nonlinear time-delay systems via ODE approximation and spectral submanifolds","authors":"Yuan Tang, Mingwu Li","doi":"10.1016/j.physd.2025.134701","DOIUrl":"10.1016/j.physd.2025.134701","url":null,"abstract":"<div><div>Time-delay dynamical systems inherently embody infinite-dimensional dynamics, thereby amplifying their complexity. This aspect is especially notable in nonlinear dynamical systems, which frequently defy analytical solutions and necessitate approximations or numerical methods. These requirements present considerable challenges for the real-time simulation and analysis of their nonlinear dynamics. To address these challenges, we present a model reduction framework for nonlinear time-delay systems using spectral submanifolds (SSMs). We first approximate the time-delay systems as ordinary differential equations (ODEs) without delay and then compute the SSMs and their associated reduced-order models (ROMs) of the ODE approximations. These SSM-based ROMs successfully predict the nonlinear dynamical behaviors of the time-delay systems, including free and forced vibrations, and accurately identify critical features such as isolated branches in the forced response curves and bifurcations of periodic and quasi-periodic orbits. The efficiency and accuracy of the ROMs are demonstrated through examples of increasing complexity.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134701"},"PeriodicalIF":2.7,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143934658","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}

引用次数: 0

Detecting causality in the frequency domain with Cross-Mapping Coherence 用交叉映射相干检测频域因果关系

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-08 DOI: 10.1016/j.physd.2025.134708

Zsigmond Benkő , Bálint Varga , Marcell Stippinger , Zoltán Somogyvári

{"title":"Detecting causality in the frequency domain with Cross-Mapping Coherence","authors":"Zsigmond Benkő , Bálint Varga , Marcell Stippinger , Zoltán Somogyvári","doi":"10.1016/j.physd.2025.134708","DOIUrl":"10.1016/j.physd.2025.134708","url":null,"abstract":"<div><div>Understanding causal relationships within a system is crucial for uncovering its underlying mechanisms. Causal discovery methods, which facilitate the construction of such models from time series data, hold the potential to significantly advance scientific and engineering fields.</div><div>This study introduces the Cross-Mapping Coherence (CMC) method, designed to reveal causal connections in the frequency domain between time series. CMC builds upon nonlinear state-space reconstruction and extends the Convergent Cross-Mapping algorithm to the frequency domain by utilizing coherence metrics for evaluation. We tested the CMC method using simulations of logistic maps, Lorenz systems, Kuramoto oscillators, and the Wilson–Cowan model of the visual cortex. CMC accurately identified the direction of causal connections in these simulated scenarios. When applied to the Wilson–Cowan model, CMC was able to disentangle feedforward alpha and feedback gamma coupling between the V1 and V4 areas, supporting the results of previous analysis.</div><div>Furthermore, CMC could detect weak connections (<span><math><mrow><mi>C</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>05</mn></mrow></math></span>), demonstrated sample efficiency (<span><math><mrow><mi>L</mi><mo>=</mo><mn>700</mn></mrow></math></span>), and maintained robustness in the presence of noise up to <span><math><mrow><mi>SNR</mi><mo>=</mo><mn>10</mn></mrow></math></span> on unidirectionally coupled logistic map systems.</div><div>In conclusion, the capability to determine directed causal influences across different frequency bands allows CMC to provide valuable insights into the dynamics of complex, nonlinear systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"477 ","pages":"Article 134708"},"PeriodicalIF":2.7,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071343","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}

引用次数: 0

The motion and mass growth of droplets with phase transitions in a homogeneous medium 均匀介质中相变液滴的运动和质量增长

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-08 DOI: 10.1016/j.physd.2025.134683

Peiyu Zhang , Aifang Qu , Hairong Yuan

引用次数: 0