| 具循环系数n 种群Volterra 系统的稳定性 |
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| 引用本文： | 刘兴臻. 具循环系数n 种群Volterra 系统的稳定性[J]. 华南师范大学学报（自然科学版）, 1999, (2): 1. |
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| 作者姓名： | 刘兴臻 |
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| 作者单位： | 广州教育学院数学系,广州,510030 |
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| 摘 要： | 本文研究了一类具循环系数ｎ种数Ｖｏｌｔｅｒｒａ系统，其中ｎ种群在同一环境中生存，且有相同的环境容纳量，利用线性化学方法和Ｌｉａｐｕｎｏｖ函数的方法讨论了正平衡点的局部稳定性和全局稳定性，从而得到该系统存在全局渐近稳定正平衡状态（全局生态平衡）的充分条件，从某种意义上来说，系统正平衡点在一定的条件下，它的局部渐近稳定性蕴涵着全局渐近稳定性。
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| 关 键 词： | Volterra系统 局部渐近稳定 全局渐近稳定 Liapunov函数 LaSalle不变原理 |
| 修稿时间： | 1998-07-02 |
THE STABILITY OF n-SPECIES VOLTERRA SYSTEM WITH RECURRENT COEFFICIENTS |
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| LIU Xingzhen. THE STABILITY OF n-SPECIES VOLTERRA SYSTEM WITH RECURRENT COEFFICIENTS[J]. Journal of South China Normal University(Natural Science Edition), 1999, 0(2): 1-29 |
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| Authors: | LIU Xingzhen |
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| Abstract: | In this paper, the stability of the positive equilibrium of n -species system with recurrent coefficients and the same carrying capacity was studied by using the technique of linearization and the method of Liapunov's function. The plenitudinous condition that the positive equilibrium of the system is global asymptotic stability was achieved. The result showed that the local asymptotic stability of the positive equilibrium under definite conditions implies, in a certain sense, the global asymptotic stability. |
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| Keywords: | Volterra system local asymptotic stability global asymptotic stability Liapunov function LaSalle theory |
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