Journal of East China Normal University(Natural Science) ›› 2022, Vol. 2022 ›› Issue (2): 24-33.doi: 10.3969/j.issn.1000-5641.2022.02.004

• Mathematics • Previous Articles     Next Articles

Codimension 3 bifurcation of a delayed predator-prey system with double Allee effect

Jianfeng JIAO(), Can CHEN*()   

  1. School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou 450046, China
  • Received:2020-10-26 Online:2022-03-25 Published:2022-03-28
  • Contact: Can CHEN;


By generalizing and using the normal form theory and center manifold theorem of delay differential equations, a class of high-codimension bifurcation problems of predator-prey systems with delay and Allee effect are investigated. Firstly, sufficient conditions for the existence of the positive equilibrium and the codimension 3 bifurcation at this positive equilibrium are established. Subsequently, the normal form of the system at the positive equilibrium is deduced. Finally, from the topological equivalence of the normal form and the original system, the bifurcation phenomenon of the original system at the positive equilibrium is analyzed.

Key words: predator-prey system, delay, triple-zero bifurcation, Allee effect

CLC Number: