Stability Analysis and Control Strategy of a Generalized Food Chain Model

Abstract

The stability analysis and control strategy for a generalized food chain model is considered in this paper. Firstly, we investigate the existence of the positive equilibrium and give the conditions of local asymptotic stability. Meanwhile, we design a feedback controller and prove the stability of the proposed model with the controller by using the Lyapunov function. Due to the addition of control, the unstable food chain system can become stable. At last, the analysis results are verified by numerical simulations. Our results may help to maintain the stability of the biological systems and avoid ecosystem imbalance.