具有差异性自食的宿主-寄生模型动力学分析  

Dynamical analysis of a host-parasite model with differential cannibalism

作　　者：刘飞燕 刘俊利[1] LIU Feiyan;LIU Junli(School of Science,Xi'an Polytechnic University,Xi'an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《延边大学学报(自然科学版)》2025年第1期6-12,共7页Journal of Yanbian University(Natural Science Edition)

基　　金：国家自然科学基金项目(11801431);陕西省自然科学基础研究计划项目(2021JM-445)。

摘　　要：研究了一个具有差异性自食的宿主-寄生模型的动力学问题.首先,利用常微分基本理论、简单的数学分析、线性化方法以及构造Dulac函数,依次证明了模型的非负有界性、平衡点的存在性、平衡点的局部及全局渐近稳定性;其次,研究了模型的一致持久性以及鞍-结点分支,并给出了模型发生鞍-结点分支的条件;最后,利用数值模拟验证了所得结果的正确性.该研究可为防治生物病虫害提供良好理论依据。This paper focuses on the dynamics of a host-parasite model with differential cannibalism.Firstly,the non-negativity and boundedness of the model,conditions for the existence of equilibria,and the local and global asymptotic stability of the equilibria are proved in turn by means of the basic theory of constant differentiation,simple mathematic alanalyses,linearization methods,and the construction of Dulac function.Secondly,the uniform persistence and saddle-node of the model are obtained and the conditions under which saddlenode bifurcation occurs in the model are given.Finally,numerical simulations were used to verify the correctness of the obtained results.This study provides a theoretical basis for biological pest control.

关 键 词：宿主-寄生模型 全局渐近稳定性 双稳态 鞍-结点分支 

分 类 号：O175.1[理学—数学]