具有反馈控制的多种群互惠系统的全局吸引性与数值模拟

Numerical Simulation and Global Attractivity of Multi-Species Cooperative System with Feedback Control

对一类具有反馈控制的非自治n种群Lotka-Volterra互惠系统进行了研究.利用微分方程比较定理,重合度理论中的延拓定理和Barbalat引理,构造适当的Lyapunov泛函,得到了一组保证系统持久性和正周期解全局吸引的充分条件.最后,利用计算机数值模拟验证了所得结论.结果表明,在所给的充分条件下,系统存在唯一全局渐近稳定的正周期解.

In this paper, a non-autonomous n-Species Lotka-Voherra cooperative system with feedback controls is investigated. By using applying Comparison Theorem of differential equation, the continuation theorem of coincidence degree theory and Barbalat Lemma, constructing a suitable Lyapunov function, a set of easily verifiable sufficient conditions are obtained to guarantee the permanent and positive periodic solution global attractivity of the system. Finally an example is given as the application of theorem. The result shows that under some sufficient conditions, there is a unique globally asymptotically stable positive periodic solution for the system.