On the Periodicity of the Rational Dynamical System Corresponding to the Vannimenus–Ising Model

IF 1.9 4区工程技术 Q3 ENGINEERING, MECHANICAL

Journal of Computational and Nonlinear Dynamics Pub Date : 2022-11-17 DOI:10.1115/1.4056133

H. Akın

引用次数: 4

Abstract

The universal behaviors of a rational dynamical system associated with the Vannimenus–Ising model having two coupling constants on a Cayley tree of order three are studied. Cobweb diagrams and related map iterates for some relevant parameters are investigated. The local stability of fixed points is discussed and illustrated through cobweb diagrams. We deal with quantitative universality, such as orbit diagrams and Lyapunov exponents for a class of rational maps. We show that our model is periodic using orbit diagrams and relevant Lyapunov exponents.

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研究了具有两个耦合常数的有理动力系统在三阶Cayley树上的普遍行为。研究了蛛网图和一些相关参数的相关映射迭代。讨论了不动点的局部稳定性，并用蛛网图加以说明。我们处理了一类有理图的数量通用性，如轨道图和李雅普诺夫指数。我们用轨道图和相关的李雅普诺夫指数来证明我们的模型是周期性的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Nonlinear Dynamics 工程技术-工程：机械

CiteScore

4.00

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.