基于Maple软件的非线性四种群捕食模型的定性分析

曲靖师范学院学报 ›› 2017, Vol. 36 ›› Issue (3): 8-10.

基于Maple软件的非线性四种群捕食模型的定性分析

王艳兵

山西师范大学临汾学院数计系,山西临汾 041000

收稿日期:2017-01-13 出版日期:2017-05-26
作者简介:王艳兵,山西师范大学临汾学院数计系助教,主要从事概率统计研究.

A Qualitative Analysis of Four Species Non-linear Volterra Prey Model Based on the Maple Software

Wang Yanbing

Department of Mathematics and Computer Science, Linfen College of Shanxi Normal University, Linfen Shanxi, 041000, China

Received:2017-01-13 Published:2017-05-26

摘要/Abstract

摘要： Volterra捕食与被捕食数学模型对研究种群增长的生态关系十分重要.在Volterra捕食模型的基础上增加一至两个新种群,建立并研究具有种内竞争,选择捕食的四种群非线性捕食模型.并对其进行定性分析及Maple软件求解,使用数值模拟描述其相图形貌,讨论模型的稳定性及其实际应用.

关键词: Maple软件, 捕食模型, 相图, 平衡点, 稳定性, 极限环

Abstract: Volterra predator-prey mathematical model is of great significance to the study of the ecological relationship in population growths. By adding two populations to the Volterra predation model, a four species non-linear predatory mode where capture leads to intra-species competition is constructed and studied on. The model is analyzed qualitatively through Maple Software to describe the morphology of its phase diagram by means of numerical simulation and to discuss the stability of the model and its practical application.

Key words: Maple Software, predator-prey model, phase diagram, equilibrium point, stability, limit cycle

中图分类号:

O175.12

王艳兵. 基于Maple软件的非线性四种群捕食模型的定性分析[J]. 曲靖师范学院学报, 2017, 36(3): 8-10.

Wang Yanbing. A Qualitative Analysis of Four Species Non-linear Volterra Prey Model Based on the Maple Software[J]. JOURNAL OF QUJING NORMAL UNIVERSITY, 2017, 36(3): 8-10.

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