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Volume 4, Number 4, 2014, Pages 419-435                                                                DOI:10.11948/2014024
Stability and Neimark-Sacker bifurcation of a semi-discrete population model
Cheng Wang,Xianyi Li
Keywords:Semi-discrete population model
Abstract:
      In this paper, a semi-discrete model is derived for a nonlinear simple population model, and its stability and bifurcation are investigated by invoking a key lemma we present. Our results display that a Neimark-Sacker bifurcation occurs in the positive fixed point of this system under certain parametric conditions. By using the Center Manifold Theorem and bifurcation theory, the stability of invariant closed orbits bifurcated is also obtained. The numerical simulation results not only show the correctness of our theoretical analysis, but also exhibit new and interesting dynamics of this system, which do not exist in its corresponding continuous version.
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