Chaos control and synchronization of a three-species food chain model via Holling functional response

Abstract

Chaos control and synchronization problem of a three-species food chain model with Holling I-type functional response is investigated. By the linearization approach, a feedback control law is developed to stabilize the model system to equilibrium points. Based on the bidirectional coupled method, chaos synchronization of the model system is studied. Numerical simulations show that the feedback control law can suppress chaos to unstable equilibrium points successfully. Further, the numeric results show that when the coupling strength 0<k<0.012, synchronization of two model systems cannot be achieved; when the coupling strength 0.012≤k<2, synchronization of two model systems is always achieved, furthermore, the larger is the coupling strength k, the smaller are the synchronization errors, the better is the effect of chaos synchronization; when the coupling strength k≥2, synchronization of two model systems can also be achieved, but the synchronization errors are bigger than that of 0.012≤k<2.