Abstract

The dynamics of the classical biological Lotka–Volterra system with a seasonality factor is investigated analytically. The original model is described by a simple Hamiltonian. To reveal the chaotic behavior in the system, the Hamiltonian is represented by a sum of a Hamiltonian that is independent of time and a number of resonances. The investigation of the interaction of these resonances using Chirikov’s resonance overlap method makes it possible to find an analytical criterion in terms of the critical values of the seasonality amplitudes under which the original system goes to chaos. The results of the study show that in the presence of a periodic perturbation (the seasonality factor in the case under consideration) the system with two dependent variables demonstrates chaotic behavior.

中文翻译：

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具有季节性因素的二维Lotka-Volterra系统混沌动力学的解析研究

摘要

对具有季节性因子的经典生物学Lotka–Volterra系统的动力学进行了分析研究。原始模型由简单的哈密顿量描述。为了揭示系统中的混沌行为，哈密顿量由与时间和共振次数无关的哈密顿量之和表示。使用Chirikov共振重叠法研究这些共振的相互作用，使得有可能根据原始系统陷入混乱的季节性幅度的临界值找到一个分析标准。研究结果表明，在存在周期性扰动（正在考虑的情况下为季节性因素）的情况下，具有两个因变量的系统表现出混沌行为。