Neimark–Sacker Bifurcation and Controlling Chaos in a Three-Species Food Chain Model through the OGY Method

Abstract

The dynamics behavior of a discrete-time three-species food chain model is investigated. By using bifurcation theory, it is shown that the equilibrium point of the system loses its stability, and the system undergoes Neimark–Sacker bifurcation, which leads to chaos as the parameter changes. The chaotic motion is controlled on the stable periodic period-1 orbit using the implementation of the hybrid control strategy. The factor affecting the control time of chaos is also studied. Numerical simulations are consistent with the theoretical analysis. The results of this research prove that the chaos control method can be extended to the higher-dimensional biological model and can be realized.