一类时滞竞争系统的定性分析

计算物理 ›› 1991, Vol. 8 ›› Issue (1): 11-18.

一类时滞竞争系统的定性分析

俞元洪, 黄维章

中国科学院应用数学研究所, 北京 100080

收稿日期:1990-06-09 出版日期:1991-03-25 发布日期:1991-03-25

QUALITATIVE ANALYSIS TO A CLASS OF DELAY-COMPETITION SYSTEMS

Yu Yuanhong, Huang Weizhang

institute of Applied Mathematics, Academia Sinica Beijing 100080, China

Received:1990-06-09 Online:1991-03-25 Published:1991-03-25

摘要/Abstract

摘要： 本文考虑具有连续时滞的Lotka-Volterra竞争系统。给出了该系统的稳定性分析。利用Hopf分支定理,我们证明了由时滞引起的不稳定性可以导致系统产生稳定的极限环。利用Birkhoff定理证明了系统可能出现循环解。最后,我们给出数值实例,验证了上述结果。

关键词: 竞争系统, 连续时滞, 分支

Abstract: In this paper the qualitative analysis of a class of Lotka-Volterra competition systems with continuous time delays are given. First, we discuss the stabilities of the systems. Then using Hopf's bifurcation theorem and Birkhoffs theorem we show that the delay-induced-instability can lead to appearance of stable limit cycles and that the systems may have recurrent solutions. Finally, some numerical examples are given in order to illustrate the results mentioned above.

Key words: competition system, continuous time delay, bifurcation

俞元洪, 黄维章. 一类时滞竞争系统的定性分析[J]. 计算物理, 1991, 8(1): 11-18.

Yu Yuanhong, Huang Weizhang. QUALITATIVE ANALYSIS TO A CLASS OF DELAY-COMPETITION SYSTEMS[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1991, 8(1): 11-18.