摘要
种群动力学作为生态系统的一个重要分支,日益受到广大学者的关注.单种群及两种群的差分生态系统的研究已取得一些重要成果,但对三种群生态差分系统的研究工作还未见发表.本文研究一类指数型三种群生物差分系统.首先,利用迭代方法及不等式技巧证明了该系统的每一个正解都是持久的和有界的;其次,利用不动点理论证明了该系统正平衡点的存在性;最后,利用线性化理论、Rouche定理及李亚普诺夫稳定性理论获得了确保该生态系统正平衡点渐近稳定的若干充分条件.所得结论推广了参考文献[20-24]中的相应结果.
Abstract
Population dynamics,as an important branch of ecosystems,is increasingly receiving attention from scholars.Significant achievements have been made in the study of differential ecosystems of single and two popu-lations,but research on differential ecosystems of three populations has not yet been published.In this paper,we study a class of exponential 3 populations biological differential systems.Firstly,we use iterative methods and in-equality techniques to prove that every positive solution of the system is persistent and bounded.Secondly,the ex-istence of a positive equilibrium point of the system is proved,using fixed point theory.Finally,using lineariza-tion theory,Rouche theorem and Lyapunov stability theory,we provide sufficient conditions for the asymptotic stability of the positive equilibrium point of the ecosystem.The obtained conclusion extends the corresponding re-sults in references[20-24].
基金项目
中央引导地方科技发展资金面上项目(22ZYZYTS0065)
成都信息工程大学科研创新团队重点项目(KYTD202226)
维普
万方数据