一类具有时滞及反馈控制的非自治非线性比率依赖食物链模型

Abstract

Abstract:

In this paper, we study a 3-species nonlinear non-autonomous ratio-dependent food chain system with delays and feedback controls. Firstly, based on the theory of delay differential inequality, some new analytical methods are developed and a suitable Lyapunov function is constructed. Secondly, sufficient conditions for the permanence and global attractivity of positive solutions for the system are obtained. Thirdly, by using the theoretical analysis and fixed point theory, the corresponding periodic systems are discussed, and the conditions for the existence, uniqueness and stability of positive periodic solutions of periodic systems are established. Moreover, we give some numerical simulations to prove that our theoretical analysis are correct. Finally, we still give an numerical example for the corresponding stochastic food chain model with multiplicative noise sources, and achieve new interesting change process of the solution for the model.

Key words: Delay, Ratio-Dependent, Feedback Control, Permanence, Global Attractive, Periodic solution

CLC Number:

O175.12

Changyou Wang,Nan Li,Tao Jiang,Qiang Yang. On a Nonlinear Non-Autonomous Ratio-Dependent Food Chain Model with Delays and Feedback Controls[J].Acta mathematica scientia,Series A, 2022, 42(1): 245-268.

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Figures/Tables 10

References 38

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On a Nonlinear Non-Autonomous Ratio-Dependent Food Chain Model with Delays and Feedback Controls

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