基于阈值策略带有扩散和不连续控制项的单物种生态模型的全局稳定性分析

摘要

In this paper, the control problem of single-species ecological model with the dis-persal is investigated via the threshold policy (TP). The positive equilibrium's existence theorem for the new model is obtained by using the uniform persistence theorem and Filippov theorem. The sufficient conditions to the uniqueness and globally asymptotical stability of the positive equilib-rium are obtained based on the new model by applying graph theoretical approach of the coupled systems and constructing Lyapunov functions method. Related results of [6] are generalized.%本文通过阈值策略(TP)研究了带有扩散的单物种生态模型的控制问题.利用一致持久性理论和Filippov理论方法,得到了新模型的正平衡点的存在性定理.通过使用耦合系统的图论方法和构建Lyapunov函数思想,得到了新模型的正平衡点唯一且全局渐进稳定的充分条件.推广了文献[6]的相关结果.