时标上动力方程的比较定理及其应用

发布时间：2018-01-01 06:01

本文关键词：时标上动力方程的比较定理及其应用　出处：《云南大学》2015年博士论文　论文类型：学位论文

【摘要】：本文中,我们首先建立了时标上带脉冲和不带脉冲的动力方程解的三类比较定理,并在时标上引入了右稠分段连续概周期函数的定义：其次.我们提出了时标上脉冲动力方程的两个Lyapunov函数型定理：然后,作为这些理论的应用,我们分别研究了三类种群系统的动力学性质.通过利用时标上动力方程解的比较定理,概周期函数的壳理论和Lyapunov函数方法,我们得到了一些保证所研究的时滞多种群Lotka-Volterra共生系统的持久性和概周期解的存在性及其全局吸引性的充分条件.在时标脉冲理论的基础上,利用时标上脉冲动力方程解的比较定理和Lyapunov函数型定理,我们进一步获得了一些使得脉冲单种群系统和时滞脉冲多种群Lotka-Volterra竞争系统的持久性和概周期解存在性及其稳定性的充分条件.即使取时标T=z或T=R.我们的结果也是新的.最后,我们给出数值实例说明所得结果是可行的.
[Abstract]:In this paper, we first establish three kinds of comparison theorems for the solutions of dynamic equations with and without impulses on time scales. Then we introduce the definition of the right dense piecewise continuous almost periodic function on the time scale: secondly, we propose two Lyapunov function type theorems for the impulsive dynamic equation on the time scale: then, as the application of these theories. In this paper, we study the dynamical properties of three kinds of population systems. By using the comparison theorem of the solutions of dynamic equations on time scales, the shell theory of almost periodic functions and the Lyapunov function method are used. We obtain some sufficient conditions to guarantee the existence of persistence and almost periodic solutions and their global attractiveness for multigroup Lotka-Volterra symbiotic systems with delay studied. On... The comparison theorem and Lyapunov function type theorem of impulsive dynamic equation on time scale are used. We further obtain some sufficient conditions for the existence and stability of the persistence and almost periodic solutions of impulsive mono-population systems and impulsive multigroup Lotka-Volterra competition systems with delays. Take the timescale Tnz or TKR. Our results are also new. Finally. A numerical example is given to show that the result is feasible.
【学位授予单位】：云南大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O175

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