一类具有双线性型两阶段结构的同类相食模型的动力学分析  

A dynamic analysis of cannibalism model with bilinear type two-stage structure

作　　者：蔺小林[1] 曹美琪 李建全 贾西北 LIN Xiao-lin;CAO Mei-qi;LI Jian-quan;JIA Xi-bei(School of Mathematics and Data Science,Shaanxi University of Science&Technology,Xi′an 710021,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021

出　　处：《陕西科技大学学报》2023年第1期202-208,共7页Journal of Shaanxi University of Science & Technology

基　　金：国家自然科学基金项目(11971281)。

摘　　要：在假定成年个体会对卵进行同类捕食和考虑卵的自然死亡率的基础上,建立了一类具有双线性型两阶段结构的同类相食模型.分别分析了不具有同类相食和具有同类相食时两种情况下模型的动力学性态.当不具有同类相食行为时,通过构造适当的Lyapunov函数证明了平衡点的全局稳定性;当具有同类相食行为时,发现同类捕食会使模型产生鞍结点分支,并通过用Dulac函数排除模型周期解的存在性,得到了模型的全局动力学性态.种群存活的两个平衡点的存在性和鞍结点分支的出现都表明种群的最终规模依赖于模型的初始条件.最后,数值模拟验证了所得分析结果的正确性.In this paper,a two-stage model with a bilinear structure was developed based on the assumption that adult individuals will feed on eggs and the natural mortality of eggs.The kinetic states of the model are analyzed separately for the two cases when there is with and without cannibalism behavior.The global stability of the equilibrium point is proved by constructing an appropriate Lyapunov function in the absence of cannibalism,and the global dynamics of the model is obtained by excluding the existence of periodic solutions by the Dulac function.The global dynamics of the model was obtained by excluding the existence of periodic solutions of the model with the Dulac function.The existence of two equilibrium points for population survival and the emergence of saddle-node bifurcation suggest that the final size of the population depends on the initial conditions of the model.Finally,the correctness of the obtained analytical results was verified by numerical simulations.

关 键 词：同类相食 平衡点 稳定性 鞍结点分支 

分 类 号：O193[理学—数学]