JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (07): 88-94.doi: 10.6040/j.issn.1671-9352.0.2013.596

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Stability and bifurcation analysis for a single population discrete model with Allee effect and delay

WU Dai-yong, ZHANG Hai   

  1. Department of Mathematics, Anqing Normal University, Anqing 246133, Anhui, China
  • Received:2013-11-28 Online:2014-07-20 Published:2014-09-15

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Abstract: We consider a single population discrete model with Allee effect and delay. By analyzing the characteristic equation of the linearized system at the positive equilibrium, we obtain the conditions ensuring the asymptotic stability of the positive equilibrium and the existence of Neimark-Sacker bifurcation, with respect to the parameter of the model. Based on the center manifold theorem and bifurcation theory, we discuss Neimark-Sacker bifurcation direction and the stability of bifurcated solutions. Finally, some numerical simulations are performed to illustrate the theoretical results.

Key words: Allee effect, delay, Neimark-Sacker bifurcation, discrete

CLC Number: 

  • O175.7
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