带有Allee效应的扩散时滞单种群模型的分支分析  

Bifurcation analysis of a diffusive single population model with Allee effect and time delay

作　　者：刘琪 常笑源 LIU Qi;CHANG Xiao-yuan(School of Sciences,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,黑龙江哈尔滨150080

出　　处：《东北师大学报（自然科学版）》2023年第2期11-15,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金青年基金资助项目(11901140);黑龙江省自然科学基金联合引导项目(LH2022A015)。

摘　　要：考虑了一类带有时滞和Allee效应的扩散单种群模型的动力学行为.通过分析特征方程根的分布,证明了平衡点的局部稳定性和全局稳定性.以时滞作为分支参数,给出了模型在正平衡点附近经历Hopf分支的存在性.应用Matlab进行数值模拟验证了所得结论,并给出解的渐近行为与初始函数的关系.The dynamics behavior of a class of diffusive single population model with time delay and Allee effect is considered.The local and global asymptotically stability of equilibrium are proved by analyzing the distribution of roots of the characteristic equation.Taking the time delay as a bifurcation parameter,the existence of Hopf bifurcation near the positive equilibrium point is given.Finally,the results are verified and the relationship between the asymptotic behavior of solutions and the initial functions is shown by numerical simulation via Matlab.

关 键 词：ALLEE效应 扩散 HOPF分支 时滞 单种群 

分 类 号：O175[理学—数学]