Journal of Nonlinear Science最新文献_第4页

Oscillatory Motions of Multiple Spikes in Three-Component Reaction–Diffusion Systems 三分量反应-扩散系统中多个尖峰的振荡运动

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-28 DOI: 10.1007/s00332-024-10058-y

Shuangquan Xie, Wen Yang, Jiaojiao Zhang

{"title":"Oscillatory Motions of Multiple Spikes in Three-Component Reaction–Diffusion Systems","authors":"Shuangquan Xie, Wen Yang, Jiaojiao Zhang","doi":"10.1007/s00332-024-10058-y","DOIUrl":"https://doi.org/10.1007/s00332-024-10058-y","url":null,"abstract":"For three specific singular perturbed three-component reaction–diffusion systems that admit N-spike solutions in one of the components on a finite domain, we present a detailed analysis for the dynamics of temporal oscillations in the spike positions. The onset of these oscillations is induced by N Hopf bifurcations with respect to the translation modes that are excited nearly simultaneously. To understand the dynamics of N spikes in the vicinity of Hopf bifurcations, we combine the center manifold reduction and the matched asymptotic method to derive a set of ordinary differential equations (ODEs) of dimension 2N describing the spikes’ locations and velocities, which can be recognized as normal forms of multiple Hopf bifurcations. The reduced ODE system then is represented in the form of linear oscillators with weakly nonlinear damping. By applying the multiple-time method, the leading order of the oscillation amplitudes is further characterized by an N-dimensional ODE system of the Stuart–Landau type. Although the leading order dynamics of these three systems are different, they have the same form after a suitable transformation. On the basis of the reduced systems for the oscillation amplitudes, we prove that there are at most (lfloor N/2 rfloor +1) stable equilibria, corresponding to (lfloor N /2 rfloor +1) types of different oscillations. This resolves an open problem proposed by Xie et al. (Nonlinearity 34(8):5708–5743, 2021) for a three-component Schnakenberg system and generalizes the results to two other classic systems. Numerical simulations are presented to verify the analytic results.\u0000","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"80 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Higher-Order Network Interactions Through Phase Reduction for Oscillators with Phase-Dependent Amplitude 通过相位缩减实现振幅随相位变化的振荡器的高阶网络互动

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-24 DOI: 10.1007/s00332-024-10053-3

Christian Bick, Tobias Böhle, Christian Kuehn

{"title":"Higher-Order Network Interactions Through Phase Reduction for Oscillators with Phase-Dependent Amplitude","authors":"Christian Bick, Tobias Böhle, Christian Kuehn","doi":"10.1007/s00332-024-10053-3","DOIUrl":"https://doi.org/10.1007/s00332-024-10053-3","url":null,"abstract":"Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction—the reduction of the dynamics onto an invariant torus—captures the emergence of collective dynamical phenomena, such as synchronization. While a first-order approximation of the dynamics on the torus may be appropriate in some situations, higher-order phase reductions become necessary, for example, when the coupling strength increases. However, these are generally hard to compute and thus they have only been derived in special cases: This includes globally coupled Stuart–Landau oscillators, where the limit cycle of the uncoupled nonlinear oscillator is circular as the amplitude is independent of the phase. We go beyond this restriction and derive second-order phase reductions for coupled oscillators for arbitrary networks of coupled nonlinear oscillators with phase-dependent amplitude, a scenario more reminiscent of real-world oscillations. We analyze how the deformation of the limit cycle affects the stability of important dynamical states, such as full synchrony and splay states. By identifying higher-order phase interaction terms with hyperedges of a hypergraph, we obtain natural classes of coupled phase oscillator dynamics on hypergraphs that adequately capture the dynamics of coupled limit cycle oscillators.\u0000","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"38 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Smooth Subsonic and Transonic Spiral Flows with Nonzero Vorticity to Steady Euler–Poisson System in Concentric Cylinders 同心圆柱体中具有非零涡度的平稳亚音速和跨音速螺旋流动与稳定欧拉-泊松系统

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-24 DOI: 10.1007/s00332-024-10057-z

Shangkun Weng, Wengang Yang, Na Zhang

引用次数: 0

The Hanging Chain Problem in the Sphere and in the Hyperbolic Plane 球面和双曲面中的悬链问题

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-19 DOI: 10.1007/s00332-024-10056-0

Rafael López

引用次数: 0

Optimal Reconstruction of Vector Fields from Data for Prediction and Uncertainty Quantification 从数据中优化重建矢量场以进行预测和不确定性量化

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-13 DOI: 10.1007/s00332-024-10047-1

Sean P. McGowan, William S. P. Robertson, Chantelle Blachut, Sanjeeva Balasuriya

{"title":"Optimal Reconstruction of Vector Fields from Data for Prediction and Uncertainty Quantification","authors":"Sean P. McGowan, William S. P. Robertson, Chantelle Blachut, Sanjeeva Balasuriya","doi":"10.1007/s00332-024-10047-1","DOIUrl":"https://doi.org/10.1007/s00332-024-10047-1","url":null,"abstract":"Predicting the evolution of dynamics from a given trajectory history of an unknown system is an important and challenging problem. This paper presents a model-free method of forecasting unknown chaotic systems through reconstructing vector fields from noisy measured data via an adaptation of optimal control methods. This technique is also applicable to partially observed systems using a Takens delay embedding approach. The algorithms are validated on the Lorenz system and the four-dimensional hyperchaotic Rössler system, and demonstrate successful predictions well beyond the Lyapunov timescale. It is found that for small datasets or datasets with large levels of noise, the prediction accuracy of partially observed systems approaches that of fully observed systems. The presented approach also allows the model-free assessment of local predictability on the attractor by evolving initial condition density through the reconstructed vector fields via estimation of the transfer operator. The method is compared to predictions made by an imperfect model which highlights the utility of model-free approaches when the only available models have significant model error. The capability of this method for reconstruction of continuous and global vector fields may be applied to model validation, forecasting of initial conditions not in the training set, and model-free filtering. ","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"25 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Discrete Nonlinear Schrödinger Equation with Linear Gain and Nonlinear Loss: The Infinite Lattice with Nonzero Boundary Conditions and Its Finite-Dimensional Approximations 具有线性增益和非线性损耗的离散非线性薛定谔方程：具有非零边界条件的无限晶格及其有限维近似值

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-11 DOI: 10.1007/s00332-024-10050-6

G. Fotopoulos, N. I. Karachalios, V. Koukouloyannis, P. Kyriazopoulos, K. Vetas

{"title":"The Discrete Nonlinear Schrödinger Equation with Linear Gain and Nonlinear Loss: The Infinite Lattice with Nonzero Boundary Conditions and Its Finite-Dimensional Approximations","authors":"G. Fotopoulos, N. I. Karachalios, V. Koukouloyannis, P. Kyriazopoulos, K. Vetas","doi":"10.1007/s00332-024-10050-6","DOIUrl":"https://doi.org/10.1007/s00332-024-10050-6","url":null,"abstract":"The study of nonlinear Schrödinger-type equations with nonzero boundary conditions introduces challenging problems both for the continuous (partial differential equation) and the discrete (lattice) counterparts. They are associated with fascinating dynamics emerging by the ubiquitous phenomenon of modulation instability. In this work, we consider the discrete nonlinear Schrödinger equation with linear gain and nonlinear loss. For the infinite lattice supplemented with nonzero boundary conditions, which describe solutions decaying on the top of a finite background, we provide a rigorous proof that for the corresponding initial boundary value problem, solutions exist for any initial condition, if and only if, the amplitude of the background has a precise value (A_*) defined by the gain-loss parameters. We argue that this essential property of this infinite lattice cannot be captured by finite lattice approximations of the problem. Commonly, such approximations are provided by lattices with periodic boundary conditions or as it is shown herein, by a modified problem closed with Dirichlet boundary conditions. For the finite-dimensional dynamical system defined by the periodic lattice, the dynamics for all initial conditions are captured by a global attractor. Analytical arguments corroborated by numerical simulations show that the global attractor is trivial, defined by a plane wave of amplitude (A_*). Thus, any instability effects or localized phenomena simulated by the finite system can be only transient prior the convergence to this trivial attractor. Aiming to simulate the dynamics of the infinite lattice as accurately as possible, we study the dynamics of localized initial conditions on the constant background and investigate the potential impact of the global asymptotic stability of the background with amplitude (A_*) in the long-time evolution of the system.\u0000","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"9 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Finite Time Blow-Up and Chemotactic Collapse in Keller–Segel Model with Signal Consumption 带有信号消耗的凯勒-西格尔模型中的有限时间膨胀和趋化崩溃

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-10 DOI: 10.1007/s00332-024-10045-3

Chunhua Jin

引用次数: 0

Sliding Mode on Tangential Sets of Filippov Systems 菲利波夫系统切向集上的滑动模式

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-09 DOI: 10.1007/s00332-024-10052-4

Tiago Carvalho, Douglas D. Novaes, Durval J. Tonon

引用次数: 0

Propagation Dynamics for a Degenerate Delayed System with Nonlocal Dispersal in Periodic Habitats 周期性生境中具有非局部散布的退化延迟系统的传播动力学

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-06 DOI: 10.1007/s00332-024-10048-0

Rong Zhou, Shi-Liang Wu, Xiong-Xiong Bao

引用次数: 0

Nonuniqueness of Generalised Weak Solutions to the Primitive and Prandtl Equations 原始方程和普朗特方程广义弱解的非唯一性

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-05-27 DOI: 10.1007/s00332-024-10032-8

Daniel W. Boutros, Simon Markfelder, Edriss S. Titi

引用次数: 0