一类关于浮游生物的时滞微分模型的局部Hopf分岔分析

摘要

主要研究时滞Lotka—Voherra模型，提出了关于浮游生物的两种群相互有增强作用的微分方程模型．将时滞工作为分岔参量，讨论了正平衡点及分岔的存在性．进一步应用规范理论与中心流形定理，判断了分岔的方向与稳定性，并给出了实例与数值模拟．%A delayed Lokta-Volterra system is mainly concerned in the paper . we propose a modified delay differential equation model of the growth of two species of plankton having competitive and stimulatory effects on each other. By regarding the delayras the bifurcation parameter, the stability of the positive equilibrium and Hopf bifurcations are investigated. Furthermore, the directions of Hopf bifurcations and the stability of the bifurcating periodic solutions are determined by applying the theory of normal form and center manifold theorem. Finally, to verify our theoretical predictions, some numerical simulations are also included at the end of this paper.