The stability of generalized Volterra equations
The stability of generalized Volterra equations
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广义 Volterra 方程的稳定性
DOI：
10.1016/0022-247x(78)90139-7
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发表时间：
1978
期刊：
影响因子：
--
通讯作者：
H. Tokumaru
中科院分区：
文献类型：
--
作者：
Y. Takeuchi;N. Adachi;H. Tokumaru
本文考虑一类特殊的广义沃尔泰拉方程组[1]，其解对任意非负初值都是非负的。拉萨尔的扩展稳定性定理用于导出非负平衡点相对于欧氏空间的某个子集稳定的条件。所得到的稳定性定理与常系数线性系统的李雅普诺夫稳定性条件有密切的关系，并且一般比迄今为止已知的条件限制较少。
In this paper, a particular type of a system of generalized Volterra equations [1], whose solutions are assured to be nonnegative for arbitrary nonnegative initial values, is considered. The extended stability theorem of LaSalle is used for deriving conditions for a nonnegative equilibrium point to be stable with respect to a certain subset of the Euclidean space. The obtained stability theorem has a close relation with Lyapunov's stability condition for linear systems with constant coefficients and is generally less restrictive than conditions known so far.