Rank-One Chaos in a Periodically Kicked Three-Species Food Chain with Time-Delay

Abstract

This paper is devoted to studying the problem of rank-one strange attractor in a three-species food chain with time-delay. The conditions for the existence of positive equilibrium and Hopf bifurcation are presented. By using the theory of rank-one maps formulated by Wang and Young in 2001, and then developed by us to the time-delayed system, the conditions for the system having rank-one strange attractor are obtained under periodically kicked system. Numerical simulations are presented to demonstrate the analytic results.