摘要
本文建立了一类在Allee效应下繁殖的三阶段结构种群动力学模型.证明了当正平衡点不存在时灭绝平衡点是全局稳定的,还得到了存在一个正平衡点和两个正平衡点的条件.当系统只存在一个正平衡点时,验证了这个正平衡点的局部渐近稳定性,进而研究了这个正平衡点全局稳定的条件.而当两个正平衡点同时存在时,证明了较小的正平衡点是不稳定的,而从较大的正平衡点可以产生Hopf分支,诱导出绝灭平衡点和正周期解双稳定现象.
In this paper,a class of three-stage structural population dynamical model with the propagation under Allee effect has been established.It is proved that the extinction equilibrium is globally stable when there is no positive equilibrium,and the conditions for the existence of one positive equilibrium and two positive equilibrium points have beenobtained.When there is only one positive equilibrium point in the system,the local asymptotic stability of this positive equilibrium point is verified,and the condition of global stability of this positive equilibrium point studied.When two positive equilibrium points exist at the same time,it is provedthat the smaller positive equilibrium point is unstable,and Hopf bifurcation can be generated from the larger positive equilibrium point,which leads to the extinction equilibrium point and the bistable phenomenon of positive periodic solution.
作者
卢越冬
王稳地
LU Yue-dong;WANG Wen-di(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)
出处
《西南师范大学学报（自然科学版）》
CAS
2021年第5期13-18,共6页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(12071381).
