| n维变时滞Lotka-Volterra系统周期正解的存在性 |
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| 引用本文： | 王震,蔺小林.n维变时滞Lotka-Volterra系统周期正解的存在性[J].数学的实践与认识,2009,39(7). |
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| 作者姓名： | 王震 蔺小林 |
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| 作者单位： | 1. 西京学院基础部,陕西,西安,710123;陕西科技大学理学院,陕西,西安,710021
2. 陕西科技大学理学院,陕西,西安,710021 |
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| 摘 要： | 基于非线性常微分方程泛函分析研究了一类变时滞n维非自治Lotka-Volterra系统周期正解的存在性,利用重合度理论建立了这类系统周期正解的存在性判据,得到了相应的充分性条件.同时对系统的持久性问题也作了分析,得到了相应的定理.最后,通过计算机仿真,对文中论述周期正解的存在性进行了佐证.
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| 关 键 词： | 周期正解 变时滞Lotka-Volterra系统 重合度理论 M矩阵 |
Existence of Positive Periodic Solution of n-Dimensional Lotka-Volterra System with Delays |
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| WANG Zhen,LIN Xiao-lin.Existence of Positive Periodic Solution of n-Dimensional Lotka-Volterra System with Delays[J].Mathematics in Practice and Theory,2009,39(7). |
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| Authors: | WANG Zhen LIN Xiao-lin |
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| Abstract: | Based on the functional analysis of nonlinear ordinary differential equation,we study a mutualism system of n-dimensional Lotka-Volterra with delays,and with the help of coincidence degree theory,we establish the existence of positive periodic solution of this system.The existence theorem is obtained in this paper,and obtained the corresponding conditions.At the same time,we analyzed the permanence of the system.Finally,Computer simulations are presented to illustrate the conclusions. |
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| Keywords: | positive periodic solution Lotka-Volterra system with delays coincidence degree theory M matrix |
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