Chaotic dynamics of a three-species food chain model

Abstract An analysis of a discrete-time food chain model is presented in this paper to investigate the effects of strong prey pressure on the chain. A bifurcation and stability theory is used to analyze equilibrium formation in system. It is shown by numerical simulations that chaos occurs as a result of the bifurcation of invariant curves following Neimark-Sacker (NS) bifurcation rules. The OGY method on stable periodic orbits of period 1 further controls chaos. Stability is achieved through iterations for chaotic motion controlled by different regulator poles. Numerical simulations are performed to examine the effects of the control method along with the results of our theoretical analysis.