离散比率依赖捕食者-猎物系统退化定点附近的定性结构

IF 1.9 3区 数学 Q1 MATHEMATICS
Jinling Yang, Shengfu Deng
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引用次数: 0

摘要

本文研究了一个离散的依赖比值的捕食者-猎物模型在退化定点附近的定性结构,其特征值为 \(\pm 1\) 。通过正态形式理论、Picard 迭代和 Takens 定理,该模型被转化为常微分系统。通过离散模型与矢量场时间一映射之间的共轭关系,可以得到定点附近离散模型的定性结构。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Qualitative Structures Near a Degenerate Fixed Point of a Discrete Ratio-Dependent Predator–Prey System

Qualitative Structures Near a Degenerate Fixed Point of a Discrete Ratio-Dependent Predator–Prey System

This paper investigates the qualitative structures of a discrete ratio-dependent predator–prey model near a degenerate fixed point whose eigenvalues are \(\pm 1\). By the normal form theory, Picard iteration and Takens’s theorem, this model is transformed into an ordinary differential system. Then the qualitative structures of this differential system near the highly degenerate equilibrium are analyzed with the blowing-up method, which yields the ones of the discrete model near the fixed point by the conjugacy between the discrete model and the time-one mapping of the vector field.

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来源期刊
Qualitative Theory of Dynamical Systems
Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.50
自引率
14.30%
发文量
130
期刊介绍: Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.
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