具有Allee效应和时滞的单种群离散模型的稳定性和分支  

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

作　　者：伍代勇[1] 张海[1] 

机构地区：[1]安庆师范学院数学与计算科学学院,安徽安庆246133

出　　处：《山东大学学报（理学版）》2014年第7期88-94,共7页Journal of Shandong University(Natural Science)

基　　金：安徽省高等学校省级自然科学研究项目(KJ2013Z186;KJ2011A197)

摘　　要：研究了一类具有Allee效应和时滞的离散单种群模型。通过分析正平衡点的特征方程,研究了正平衡点的稳定性和Neimark-Sacker分支的存在性。并基于中心流形定理和分支理论,讨论了Neimark-Sacker分支方向和稳定性。最后通过数值模拟验证了结论的可行性。We consider a single population discrete model with Allee effect and delay.By analyzing the characteristic e-quation 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.

关 键 词：ALLEE效应 Neimark-Sacker分支 时滞 离散 

分 类 号：O175.7[理学—数学]