摘要
研究一类带恐惧因子和强Allee效应的捕食者-食饵扩散模型的Hopf分支问题.首先分析非负平衡点的局部渐近稳定性,然后以捕获者死亡率作为Hopf分支参数,给出了扩散模型Hopf分支存在的条件;利用中心流形定理和规范型理论,讨论了扩散系统Hopf分支的方向及分支周期解的稳定性.最后利用数值模拟验证了所得结论.
The Hopf bifurcation of a diffusive predator-prey model with fear factors and strong Allee effects is considered.Firstly,the local asymptotic stability of the non-negative equilibrium points is given.Secondly,by choosing the predator s natural growth rate as a bifurcation parameter,the existence conditions of Hopf bifurcation for the model are obtained.Next,the Hopf branch direction of diffusive system and the conditions for the stability of periodic solutions are discussed by using the center manifold theory and the normal form method.Finally,some numerical simulations are presented to verify these theoretical results.
作者
伏升茂
苏发儒
FU Sheng-mao;SU Fa-ru(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)
出处
《西北师范大学学报（自然科学版）》
CAS
北大核心
2019年第3期14-20,共7页
Journal of Northwest Normal University(Natural Science)
基金
国家自然科学基金资助项目(11361055
11761063)
