Abstract
A predator‐prey model with disease in prey, Ivlev‐type functional response, and impulsive effects is proposed. By using Floquet theory and small amplitude perturbation skill, sufficient conditions of the existence and global stability of susceptible pest‐eradication periodic solution are obtained. By impulsive comparison theorem, conditions ensuring the permanence of the system are established. Examples and simulation are given to show the complex dynamics for the key parameters.
Highlights
It is well known that many evolution processes are characterized by the fact that at certain moments their stage changes abruptly
0.8 α periodic pesticide spraying on all species and periodically releasing predator at fixed different time
Our results show that the susceptible prey is either extinct or permanent, that is, when the stability of extinct equilibrium is lose, the system becomes permanent
Summary
It is well known that many evolution processes are characterized by the fact that at certain moments their stage changes abruptly. Considering the influence of periodic pesticide spraying on all species and periodically releasing predator at fixed different time, authors 1 proposed and studied the following predator-prey system with impulsive perturbation and Ivlev-type functional response: xt ax t. In this paper, we are concerned with the following predator-prey model with complex influence of disease in prey, Ivlev-type functional response, and impulsive perturbation as follows:. By using Floquet theory, comparison method of impulsive differential equation, and numerical analysis skill, we aim to study the dynamics of 1.2 with disease in prey, Ivlevtype functional response, and impulsive effects.
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