The stability and bifurcation analysis of a discrete Holling-Tanner model

Advances in Difference Equations

Zongmin Yue¹  Hui Cao³  Yicang Zhou⁵ 

[1]Technology, Xi’

[2]Department of Applied Mathematics, Xi’

[3]Department of Mathematics, Shaanxi University of Science &

[4]an Jiaotong University, Xi’

[5]an, China

关键词: discrete Holling-Tanner model;    flip bifurcation;    Neimark-Sacker bifurcation;    stability;   

DOI  :  10.1186/1687-1847-2013-330

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A discrete predator-prey model with Holling-Tanner functional response is formulated and studied. The existence of the positive equilibrium and its stability are investigated. More attention is paid to the existence of a flip bifurcation and a Neimark-Sacker bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.

【 授权许可】

CC BY