Hopf bifurcation analysis in a predator–prey model with two time delays and stage structure for the prey

• Main Authors: Miao Peng, Zhengdi Zhang
• Format: Article
• Language: English
• Published: SpringerOpen 2018-07-01
• Series: Advances in Difference Equations
• Subjects: Hopf bifurcation; Predator–prey model; Time delay; Stage structure; Local stability
• Online Access: http://link.springer.com/article/10.1186/s13662-018-1705-9

Abstract In this paper, a stage-structured predator–prey model with Holling type III functional response and two time delays is investigated. By analyzing the associated characteristic equation, its local stability and the existence of Hopf bifurcation with respect to both delays are studied. Based on the normal form method and center manifold theorem, the explicit formulas are derived to determine the direction of Hopf bifurcation and the stability of bifurcating period solutions. Finally, the effectiveness of theoretical analysis is verified via numerical simulations. This study may be helpful in understanding the behavior of ecological environment.