Dynamics of an impulsive control system which prey species share a common predator |
| |
Authors: | Pei Yongzhen Yang Yong Li Changguo |
| |
Institution: | aSchool of Science, Tianjin Polytechnic University, Tianjin 300161, PR China;bDepartment of Basic Science of Institute of Military Traffic, Tianjin 300161, PR China |
| |
Abstract: | In an ecosystem multiple prey species often share a common predator and the interactions between the preys are neutral. In view of these facts and based on a multiple species prey–predator system with Holling IV and II functional responses, an impulsive differential equation to model the process of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated. It is proved that there exists a locally asymptotically stable pest-eradication periodic solution under the assumption that the impulsive period is less than some critical value (or the release amount of the predator is greater than another critical value). Permanence conditions are established when the impulsive period is greater than another critical value (or the release amount of the predator is less than some critical value). Numerical results show that the system we consider has more complex dynamics including period solution, quasi-periodic oscillation, chaos, intermittency and crises. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|