含扩散的prey-predator系统的Hopf分支解

THE SOLUTIONS OF HOPF BIFURCATION FOR THE PREY-PREDATOR SYSTEM WITH DIFFUSION

本文讨论一类含扩散的prey-predator系统的Hopf分支问题,研究了扩散项对系统的平衡态的稳定性的影响。以捕食种群的固有减少率为参数,得到了Hopf分支产生的条件以及分支解的近似表达式,并在取定其它参数时,讨论了分支的方向及其稳定性。所用的方法是谱分析,中心流形定理及Hopf分支理论。

In this paper the solution of Hopf-bifurcationfora Prey-Predatorsystem with diffusion is considered, the influence of diffusion for stability of the system, and the conditions which raise the Hopf-bifurcation for parameter γ (mortality of predator in absence of prey) are studied, an approximation form of the periodic solution is also given. Results are obtained by the use of spectral analysis, center manifold and Hopf—bifurcation theory.