一类具有Beddington-DeAngelis功能反应的离散竞争反馈控制系统的持久性与稳定性

Permanence and global stability of a discrete competition feedback-control system with Beddington-DeAngelis functional response

针对一类具有Beddington-DeAngelis功能反应的离散竞争系统,考虑到存在外界干扰,通过引进反馈控制,利用差分方程的比较原理,研究该系统一致持久性的充分条件;通过适当的分析技巧,构造离散的Lyapunov函数,利用微分方程中值定理,得到了该系统的正平衡点全局渐近稳定性的充分条件.由此充分说明了该系统的持久性与稳定性不受外界扰动的影响.

For a class of discrete competition system with Beddington-DeAngelis functional response, taking the existence of outside interference into account, sufficient conditions for the uniform persistence of the system is studied by introducing feedback control and using the comparison theorem of difference equations. Through appropriate analysis techniques, constructing suitable discrete Lyapunov function and using mean value theorem of differentials, sufficient conditions are obtained for global asymptotic stability of the system＇s positive equilibrium. Therefore, it is fully illuminated that the persistence and stability of the system are not influenced by outside perturbations.