对某类最大加动态系统中超离散极限循环的概括

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Mathematical Physics Pub Date : 2024-08-30 DOI:10.1063/5.0203186

Shousuke Ohmori, Yoshihiro Yamazaki

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引用次数: 0

摘要

研究了超离散极限循环的广义 max-plus 模型的动力学特性。该模型包括负反馈模型和塞尔科夫模型。它表现出 Neimark-Sacker 分岔，并具有稳定和不稳定的超离散极限循环。极限循环中的离散状态数可以通过分析确定，并提出了其近似关系。此外，还讨论了 max-plus 模型与边界碰撞分岔的二维法线形式之间的关系。

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A generalization for ultradiscrete limit cycles in a certain type of max-plus dynamical systems

Dynamical properties of a generalized max-plus model for ultradiscrete limit cycles are investigated. This model includes both the negative feedback model and the Sel’kov model. It exhibits the Neimark–Sacker bifurcation, and possesses stable and unstable ultradiscrete limit cycles. The number of discrete states in the limit cycles can be analytically determined and its approximate relation is proposed. Additionally, relationship between the max-plus model and the two-dimensional normal form of the border collision bifurcation is discussed.

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来源期刊

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.