STABILITY AND NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE POPULATION MODEL

Cheng Wang; Xianyi Li

doi:10.11948/2014024

2014 Volume 4 Issue 4

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Cheng Wang, Xianyi Li. STABILITY AND NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE POPULATION MODEL[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 419-435. doi: 10.11948/2014024

Citation:

Cheng Wang, Xianyi Li. STABILITY AND NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE POPULATION MODEL[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 419-435. doi: 10.11948/2014024

STABILITY AND NEIMARK-SACKER BIFURCATION OF A SEMI-DISCRETE POPULATION MODEL

College of Mathematical Science, Yangzhou University, Yangzhou, 225002, China

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Abstract

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 NeimarkSacker 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.
- Semi-discrete population model /
- stability /
- Neimark-Sacker bifurcation /
- Lyapunov exponent /
- Chaos
MSC: 39A11;37F45;37G35

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