Nonlinear Dynamics

, Volume 68, Issue 1, pp 23–42

A delayed predator–prey model with strong Allee effect in prey population growth

  • Pallav Jyoti Pal
  • Tapan Saha
  • Moitri Sen
  • Malay Banerjee
Original Paper

DOI: 10.1007/s11071-011-0201-5

Cite this article as:
Pal, P.J., Saha, T., Sen, M. et al. Nonlinear Dyn (2012) 68: 23. doi:10.1007/s11071-011-0201-5

Abstract

In this paper, we consider a delayed predator-prey system with intraspecific competition among predator and a strong Allee effect in prey population growth. Using the delay as bifurcation parameter, we investigate the stability of coexisting equilibrium point and show that Hopf-bifurcation can occur when the discrete delay crosses some critical magnitude. The direction of the Hopf-bifurcating periodic solution and its stability are determined by applying the normal form method and the centre manifold theory. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using the global Hopf-bifurcation result of Wu ({Trans. Am. Math. Soc.} 350:4799–4838, 1998) for functional differential equations, we establish the global existence of periodic solutions. Numerical simulations are carried out to validate the analytical findings.

Keywords

Predator–prey model Time delay Allee effect Local Hopf bifurcation Global continuation 

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Pallav Jyoti Pal
    • 1
  • Tapan Saha
    • 2
  • Moitri Sen
    • 3
  • Malay Banerjee
    • 3
  1. 1.Department of MathematicsDumkal Institute of Engineering & TechnologyBasantapurIndia
  2. 2.Department of MathematicsHaldia Government CollegeEast MidnaporeIndia
  3. 3.Department of Mathematics and StatisticsIndian Institute of Technology KanpurKanpurIndia

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