Dynamic behaviors of the periodic Lotka–Volterra competing system with impulsive perturbations
Dynamic behaviors of the periodic Lotka–Volterra competing system with impulsive perturbations
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DOI：
10.1016/j.chaos.2005.09.059
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发表时间：
2007
影响因子：
7.8
通讯作者：
Bing Liu;Z. Teng;Wanbo Liu
中科院分区：
文献类型：
--
作者：
Bing Liu;Z. Teng;Wanbo Liu
本文研究了一类具有脉冲扰动的经典周期Lotka-Volterra竞争系统。利用线性周期脉冲方程的Floquet理论，给出了平凡周期解和半平凡周期解线性稳定的条件，并通过引入的一些抽象单调迭代格式，给出了这些解全局稳定的条件，并利用这些条件得到了持久性的充分条件。利用重合度法，导出了至少存在一个严格正周期解的条件。通过具体算例和数值模拟验证了理论结果。结果表明，所考虑的系统的动力学行为与没有脉冲的系统有很大的不同。
In this paper, we investigate a classical periodic Lotka–Volterra competing system with impulsive perturbations. The conditions for the linear stability of trivial periodic solution and semi-trivial periodic solutions are given by applying Floquet theory of linear periodic impulsive equation, and we also give the conditions for the global stability of these solutions as a consequence of some abstract monotone iterative schemes introduced in this paper, which will be also used to get some sufficient conditions for persistence. By using the method of coincidence degree, the conditions for the existence of at least one strictly positive (componentwise) periodic solution are derived. The theoretical results are confirmed by a specific example and numerical simulations. It shows that the dynamic behaviors of the system we consider are quite different from the corresponding system without pulses.