THE GEOMETRICAL ANALYSIS OF A PREDATOR-PREY MODEL WITH MULTI-STATE DEPENDENT IMPULSES

Jianmei Wang; Huidong Cheng; Yan Li; Xiaoning Zhang

doi:10.11948/2018.427

2018 Volume 8 Issue 2

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Jianmei Wang, Huidong Cheng, Yan Li, Xiaoning Zhang. THE GEOMETRICAL ANALYSIS OF A PREDATOR-PREY MODEL WITH MULTI-STATE DEPENDENT IMPULSES[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 427-442. doi: 10.11948/2018.427

Citation:

Jianmei Wang, Huidong Cheng, Yan Li, Xiaoning Zhang. THE GEOMETRICAL ANALYSIS OF A PREDATOR-PREY MODEL WITH MULTI-STATE DEPENDENT IMPULSES[J]. Journal of Applied Analysis & Computation, 2018, 8(2): 427-442. doi: 10.11948/2018.427

THE GEOMETRICAL ANALYSIS OF A PREDATOR-PREY MODEL WITH MULTI-STATE DEPENDENT IMPULSES

1 College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China;
2 College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China

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Abstract

Abstract

Starting from the practical problems of integrated pest management, we establish a predator-prey model for pest control with multi-state dependent impulsive, which adopts two different control methods for two different thresholds. By applying geometry theory of impulsive differential equations and the successor function, we obtain the existence of order one periodic solution. Then the stability of the order one periodic solution is studied by analogue of the Poincaré criterion. Finally, some numerical simulations are exerted to show the feasibility of the results.
- Semi-continuous dynamic system /
- successor function /
- order one periodic solution /
- stability
MSC: 34D20;34C25;34A37;92B05

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References

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