三类指数型差分方程稳定性研究
首发时间:2020-04-03
摘要:差分方程是微分方程与动力系统研究中的重要分支。差分方程的应用与自然科学的研究有着密切的联系,其中指数型差分方程就出现在种群动力学中。本文就是在此基础上分别对三类指数型差分方程系统的动力学性质进行研究。研究方法主要分两部分,首先讨论各个系统平衡点的存在唯一性以及正解的收敛性,然后讨论平衡点的渐进稳定性,从而得出各个系统平衡点全局渐进时其中参数所满足的条件。本文所探究的指数型差分方程系统均是描述多种种群相互作用的生物模型,不仅在理论研究上突破维数的限制,建立出更为详尽的生物模型理论,而且为探索更为潜在的生态机制提供理论支持。
For information in English, please click here
Study on Stability of Three Kinds of Exponential Difference Equations
Abstract:Difference equation is an important branch of differential equation and dynamic s-\\ystem research. The application of difference equation is closely related to the research of nat-\\ural science, among which exponential difference equation appears in population dynamics. O-\\n this basis, the dynamic properties of three types of exponential difference equation systems are studied in this paper. The research method is mainly divided into two parts. First, the ex-\\istence and uniqueness of the equilibrium point of each system and the convergence of positiv-\\e solutions are discussed. Then, the asymptotic stability of the equilibrium point is discussed. Thus, the conditions that the parameters satisfy when the equilibrium point of each system is globally asymptotic are obtained. The exponential difference equation systems explored in thi-\\s paper are all biological models describing the interaction of various populations. They not o-\\nly break through the limitation of dimensionality in theoretical research and establish more detailed biological model theories, but also provide theoretical support for exploring more po-\\tential ecological mechanisms.
Keywords: Difference equation Equilibrium point Convergence Stability
基金:
引用
No.****
同行评议
勘误表
三类指数型差分方程稳定性研究
评论
全部评论0/1000