Complex Dynamics of an Impulsive Control System in which Predator Species Share a Common Prey

In an ecosystem, multiple predator species often share a common prey and the interactions between the predators are neutral. In view of this fact, we propose a three-species prey-predator system with the functional responses and impulsive controls to model the process of pest management. It is proved that the system has a locally stable pest-eradication periodic solution under the assumption that the impulsive period is less than some critical value. In particular, two single control strategies (biological control alone or chemical control alone) are proposed. Finally, we compare three pest control strategies and find that if we choose narrow-spectrum pesticides that are targeted to a specific pest's life cycle to kill the pest, then the combined strategy is preferable. Numerical results show that our system has complex dynamics including period-doubling bifurcation, quasi-periodic oscillation, chaos, intermittency and crises.