Control optimization and homoclinic bifurcation of a prey–predator model with ratio-dependent
TL;DR: In this paper, a predator-prey model with ratio-dependent and impulsive state feedback control is constructed, where the pest growth rate is related to an Allee effect.
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Abstract: In this paper, a predator–prey model with ratio-dependent and impulsive state feedback control is constructed, where the pest growth rate is related to an Allee effect. Firstly, the existence condition of the homoclinic cycle is obtained by analyzing the control parameter q. The existence, uniqueness and asymptotic stability of the periodic orbit are discussed by using the geometric theory of the differential equations, the method of successor functions and analog of the Poincare criterion. Secondly, we formulate a control optimization with a minimal total cost in pest management, and we obtain an optimal economic threshold. Finally, we verify the main results by numerical simulation.
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Citations
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Global dynamic behavior of a predator-prey model under ratio-dependent state impulsive control
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Optimization of an integrated feedback control for a pest management predator-prey model.
TL;DR: To obtain the minimum cost per period of controlling pests, the optimization problem is proposed and the optimal threshold is calculated and the feasibility of the Leslie-Gower predator-prey model is proved by numerical simulation of a concrete example.
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Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay
Zhenzhen Shi,Yaning Li,Huidong Cheng +2 more
- 01 Jul 2019
TL;DR: The singularity of this model is qualitatively analyzed, the existence and uniqueness of order-one periodic orbit are considered, and the stability of periodic orbit is verified to ensure a certain robustness of this control.
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References
Periodic solution and control optimization of a prey-predator model with two types of harvesting
TL;DR: In this paper, the existence, uniqueness and asymptotic stability of the order-1 periodic solution are discussed and numerical simulations with an example are given to illustrate the feasibility of the theorem-related results.
Geometrical analysis and control optimization of a predator-prey model with multi state-dependent impulse
TL;DR: In this article, a predator-prey model with Holling type-I functional response and multi state impulsive feedback control is established, where the intensity of pesticide spraying and the release amount of natural enemies are linearly dependent on the given threshold in the second impulse.
Global dynamics of an age-structured in-host viral infection model with humoral immunity
Liangchen Li,Rui Xu +1 more
TL;DR: In this paper, an age-structured in-host viral infection model with humoral immunity, consisting of partial differential and ordinary differential equations, was investigated, and the local stability of an infection-free steady state, an immune-inactivated infected steady state and an immuneactivated infected infection steady state was established.
Periodic solution of the system with impulsive state feedback control
TL;DR: In this article, the stability of the order-1 periodic solution of semi-continuous systems with impulsive state feedback control was investigated and sufficient conditions for the existence of the solution were derived by differential equation geometry theory and successor function.
39
Geometric approach to the stability analysis of the periodic solution in a semi-continuous dynamic system
TL;DR: In this paper, a geometric approach is applied to analyze the stability of the positive order-one periodic solution in semi-continuous dynamic systems, and sufficient conditions to insure the existence of the periodic solution are provided.
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