Bifurcation analysis of a three-species ecological system with time delay and harvesting

Abstract

Abstract This paper deals with a three-species ecological system with time delay and harvesting. Sufficient conditions guaranteeing the local stability and the occurrence of Hopf bifurcation for the system are obtained. Further, the properties of Hopf bifurcation are investigated using the center manifold theorem and normal form theory. Computer simulations are carried out to illustrate the theoretical predictions. Finally, biological meaning and a conclusion are presented.

Keywords

• delay
• Hopf bifurcation
• ecological system
• periodic solution