一类脉冲多种群生态系统的动力学性质

Dynamical Behaviors for Multi-Species Ecosystems with Impulsive Effects

研究一类脉冲效应的多种群生态系统的动力学性质.利用脉冲型Barbalet引理和比较原理,讨论了该系统的正不变集和最终有界性质,从而获得系统是永久持续生存的.在此基础上,借助于Poincar啨映射和Brouwer不动点定理,讨论了系统周期解存在性及其范围.最后,利用Lyapunov方法和脉冲型Barbalet引理,得到周期解的全局渐近稳定性和唯一性.

The dynamical behaviors for multi-species ecosystems with impulsive effects are investigated.The positive invariant sets and ultimate boundedness are discussed by using impulsive type Barbalet lemma and comparison theorem,and so the persistence holds for the ecosystems.Based on these results,the existence and estimation of period solutions are discussed via Poincaré mapping and Brouwer fixed point theorem.Finally,by employing Lyapunov approach and impulsive Barbalet lemma,the global asymptotical stability and uniqueness of the periodic solution are derived.