贝弗顿-霍尔特-里克尔竞争模型的全局吸引子及其一维和二维结构

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2024-09-18 DOI:10.1016/j.physd.2024.134354

Qi Cheng , Jun Zhang , Weinian Zhang

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引用次数: 0

摘要

贝弗顿-霍尔特-里克尔竞争模型是一个平面差分系统，用于描述个体间的种内竞争和种间竞争。已知的著作研究了某些情况下平衡点的稳定性，证明了当不存在内部平衡点时存在稳定的 2 周期点，并在数值上发现了在某些适当参数下具有谜状吸引盆地的吸引子。在本文中，我们证明了全局吸引子的存在，并完整地描述了除某些高退化情况外所有均衡的定性和分岔。此外，我们还得到了全局吸引子的不同类型的一维或二维结构，而这些结构在已知工作中是没有考虑到的。

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Global attractor and its 1D and 2D structures of Beverton–Holt Ricker competition model

Beverton–Holt Ricker competition model is a planar difference system that describes intraspecific competition among individuals and interspecific competition. Known works investigated the stability of equilibria in some cases, showed the existence of stable 2-periodic points when there are no interior equilibria, and found numerically an attractor with riddled basin of attraction for some appropriate parameters. In this paper, we prove the existence of the global attractor, and give a complete description on qualitative properties and bifurcations of all equilibria except for some cases of high degeneracy. Moreover, we obtain different kinds of 1-dimensional or 2-dimensional structures of the global attractor, which were not considered in the known work.

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.