状态反馈脉冲控制Holling-Tanner系统周期解的存在性*

Abstract

Abstract: In this paper, we investigate the Holling-Tanner model with state feedback impulsive control. On the premise that the continuous system has a unique limit cycle and the positive equilibrium point is an unstable focus point, by means of the geometry theory of semi-continuous dynamic system, successor function method and mathematical analysis method, we obtain sufficient conditions for the existence, uniqueness and orbital stability of order 1 periodic solution of the impulsive system. The main conclusions are verified by numerical simulation. Moreover, the numerical results show that the impulsive system has order k periodic solutions within the limit cycle for some parameters.

Key words: Holling-Tanner model, Limit cycle, Successor function, Order 1 periodic solution, State feedback impulsive control

CLC Number:

O175

Liang Zhiqing, Zeng Xiaping, Zhou Zewen, Pang Guoping, Huang Junhua. Existence of Periodic Solution of Holling-Tanner System with State Feedback Impulsive Control[J].Acta mathematica scientia,Series A, 2018, 38(1): 174-189.

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References

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Existence of Periodic Solution of Holling-Tanner System with State Feedback Impulsive Control

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