基于成熟阶段密度制约的同类相食模型的动力学分析  

Dynamics Analysis of Cannibalistic Model With Density Dependence in Mature Stage

作　　者：贾西北 蔺小林[1] 李建全 曹美琪 JIA Xibei;LIN Xiaolin;LI Jianquan;CAO Meiqi(School of Mathematics&Data Science,Shaanxi University of Science&Technology,Xi’an 710021,P.R.China)

机构地区：[1]陕西科技大学数学与数据科学学院,西安710021

出　　处：《应用数学和力学》2023年第3期355-366,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11971281)。

摘　　要：在考虑成熟阶段具有密度制约的基础上,建立了一类具有卵-成熟阶段的同类相食模型.该文从两个方面讨论了模型的动力学性态:当种群不存在同类相食时,构造Lyapunov函数证明平衡点的全局渐近稳定性;当种群存在同类相食时,利用中心流形定理证明同类相食使模型产生鞍结点分支,通过构造Dulac函数说明在二维自治系统中不存在极限环,得到了平衡点的全局稳定性.最后,利用数值模拟验证了所得相应结果的正确性.In view of the density dependence of mature individuals,a two-stage cannibalistic model with the egg-to-maturity stage was established.The dynamic behaviors of the model were discussed from two aspects.In the case without cannibalism,the global asymptotic stability of the equilibrium points was proved through construction of the Lyapunov function,while in the case with cannibalism,the existence of saddle-node bifurcation due to cannibalism was proved with the center manifold theorem.Through construction of the Dulac function,nonexistence of the limit cycle in the two-dimensional autonomous system was elucidated,and therefore,the global stability of the equilibrium points was obtained.Finally,the theoretical results were verified through numerical simulation.

关 键 词：同类相食 鞍结点分支 密度制约 DULAC函数 

分 类 号：O175.13[理学—数学]