Dynamics of an ecological model with impulsive control strategy and distributed time delay
Dynamics of an ecological model with impulsive control strategy and distributed time delay
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DOI：
10.1016/j.matcom.2011.08.009
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发表时间：
2012-04
期刊：
影响因子：
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通讯作者：
Min Zhao;Xitao Wang;Hengguo Yu;Jun Zhu
中科院分区：
文献类型：
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作者：
Min Zhao;Xitao Wang;Hengguo Yu;Jun Zhu
本文利用生态学和常微分方程的理论和方法，定义了具有脉冲控制策略和分布时滞的生态模型。利用脉冲方程理论、小幅度扰动和比较技术，确定了保证猎物（x）和捕食者（y）根除周期解的全局渐近稳定性的条件。事实证明，该系统是永久性的。此外，还对脉冲扰动对固有振荡的影响进行了数值研究，固有振荡表现出丰富的动力学特征，包括周期减半分岔、混沌窄窗或宽窗以及混沌危机。最大李雅普诺夫指数的计算证实了模型的混沌动态行为。所有这些结果可能有助于研究生态系统的动态复杂性。
In this paper, using the theories and methods of ecology and ordinary differential equations, an ecological model with an impulsive control strategy and a distributed time delay is defined. Using the theory of the impulsive equation, small-amplitude perturbations, and comparative techniques, a condition is identified which guarantees the global asymptotic stability of the prey-(x) and predator-(y) eradication periodic solution. It is proved that the system is permanent. Furthermore, the influences of impulsive perturbations on the inherent oscillation are studied numerically, an oscillation which exhibits rich dynamics including period-halving bifurcation, chaotic narrow or wide windows, and chaotic crises. Computation of the largest Lyapunov exponent confirms the chaotic dynamic behavior of the model. All these results may be useful for study of the dynamic complexity of ecosystems.