Hopf bifurcations in a three-species food chain system with multiple delays

Abstract

This paper is concerned with a three-species Lotka-Volterra food chain system with multiple delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the stability of the positive equilibrium and existence of Hopf bifurcations are investigated. Furthermore, the direction of bifurcations and the stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.

Keywords

• three-species food chain
• delay
• hopf bifurcation
• center manifold
• periodic solutions
• 34c23
• 34c25