【摘要】 研究了具有扩散项的比率依赖型捕食食饵系统.为了研究系统在正平衡点的稳定性和局部Hopf分支,分析系统在正平衡点处线性化部分的特征方程,这样得到了系统在正平衡点的渐进稳定性.证明了当时滞穿过某一临界值时,正平衡点失去了稳定性.也得到了Hopf分支的存在性.更多还原

【Abstract】 The ratio-dependent predator-prey diffusion system is studied.In order to investigate the stability of the positive constant steady state and Hopf bifurcation,the system at the positive constant steady state is linearized and the associated characteristic equation is analyzed,and the asymptotic stability of the positive equilibrium is obtained.It is proved that the positive constant steady state loses stability as the delays cross certain values.The existence of Hopf bifurcation is obtained.更多还原