N种群的互惠模型的全局渐近稳定性

Global Asymptotic Stability of N-species Cooperative Reaction-Diffusion Systems With Time Delays

文章研究了具有时滞N-物种互惠反应扩散系统及其相应的常微分系统。利用一般反应扩散系统的上下解方法,得到了解的存在性和平衡态方程正解的全局渐近稳定性的充分条件。这个结果导致了互惠反应扩散系统的持久性,平凡解和所有半平凡解的不稳定性和不存在非一致平衡解。

This paper is concerned with N - species time - delayed Lotka - Volterra cooperative reaction - diffusion systems and their corresponding ordinary differential systems without diffusion. Adopting the method of upper and lower solutions for a more general reaction - diffusion system, the initial and boundary conditions of reaction - diffusion of solutions and glo sys bal tems with time delays are dealt with to obtain the sufficient conditions for the existence asymptotic stability of a positive steady - state solution. The result leads to the permanence of the cooperative systems, the instability of the trivial and all forms of semitrivial solutions, and the nonexistence of nonuniform steady- state solutions