积分差分方程的数值动力学:正向动力学和回拉吸引子

IF 1 Q3 Engineering

Journal of Computational Dynamics Pub Date : 2022-05-11 DOI:10.3934/jcd.2023003

H. Huynh, P. Kloeden, Christian Potzsche

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引用次数: 0

摘要

为了确定非自治方程的动力学，需要了解它们的前向和后向行为。为此，我们给出了度量空间中一般非自治差分方程的吸引不变量集存在的充分判据。此外，还证明了前向吸引子和后向吸引子以及前向极限集都是持续存在的，并且后向极限集和后向极限集在摄动下甚至收敛。作为具体应用，我们研究了配置型空间离散化下的积分差分方程。

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Numerical dynamics of integrodifference equations: Forward dynamics and pullback attractors

In order to determine the dynamics of nonautonomous equations both their forward and pullback behavior need to be understood. For this reason we provide sufficient criteria for the existence of such attracting invariant sets in a general setting of nonautonomous difference equations in metric spaces. In addition it is shown that both forward and pullback attractors, as well as forward limit sets persist and that the latter two notions even converge under perturbation. As concrete application, we study integrodifference equation under spatial discretization of collocation type.

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来源期刊

Journal of Computational Dynamics Engineering-Computational Mechanics

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： JCD is focused on the intersection of computation with deterministic and stochastic dynamics. The mission of the journal is to publish papers that explore new computational methods for analyzing dynamic problems or use novel dynamical methods to improve computation. The subject matter of JCD includes both fundamental mathematical contributions and applications to problems from science and engineering. A non-exhaustive list of topics includes * Computation of phase-space structures and bifurcations * Multi-time-scale methods * Structure-preserving integration * Nonlinear and stochastic model reduction * Set-valued numerical techniques * Network and distributed dynamics JCD includes both original research and survey papers that give a detailed and illuminating treatment of an important area of current interest. The editorial board of JCD consists of world-leading researchers from mathematics, engineering, and science, all of whom are experts in both computational methods and the theory of dynamical systems.