Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect

Allee effect, as an important biological phenomenon, has been considered in many ecosystems, whereas, its influence on interactions of three or more species is little investigated. In this paper we modify a three-species Leslie-Gower type food chain system by incorporating the strong Allee effect into the source. Our results show that the existence of Allee effect contributes to the occurrence of more complex dynamics of the system, including Hopf, saddle-node, transcritical, saddle-node-Hopf, period-doubling, and period-halving bifurcations and chaos.