lp-非线性测度_ Cohen-Grossberg神经网络稳定性分析的一种新方法.doc

lp-非线性测度: Cohen-Grossberg神经网络稳定
性分析的一种新方法
万安华
中山大学数学与计算科学学院,广州 510275
摘要:推广了非线性测度概念,建立了研究一般非线性系统平衡点存在性和惟一性的一种新方
法。作为应用,证明了Cohen-Grossberg神经网络平衡点的存在惟一性。接下来,通过定义一
个新颖的Lyapunov函数,在更为一般的假设下建立了神经网络指数稳定性的充分条件,统一
和推广了一些已有结果。
关键词:lp-非线性测度;指数稳定性;Cohen-Grossberg神经网络;指数衰减估计
中图分类号:
lp-Nonlinear Measure: A New Approach to
Stability Analysis of Cohen-Grossberg Neural
Networks
Wan An-Hua
School of Mathematics putational Science, Sun Yat-sen University, Guangzhou
510275
Abstract: The nonlinear measure notion is extended, and then a new approach is
established to analyze the existence and uniqueness of an equilibrium of general nonlinear
systems. As a consequence, a series of new conditions for the existence and uniqueness of
equilibrium point of Cohen-works is derived. Moreover, by defining a novel
Lyapunov functional, a series of sufficient conditions for the exponential stability of the
networks is proved under more general assumptions. Compared to existing work, the proved
stability results are less restrictive, and hence unify and/or extend most existing results.
Key words: lp-nonlinear measure; Exponential stability; Cohen-Grossberg works;
Exponential decay estimation.
基金项目: 高等学校博士学科点专项科研基金(20090171120022)资助课题.
作者简介: 万安华(1976-),女,副教授,主要研究方向:非线性控制。
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Introduction
Cohen-Grossberg work is a recurrently work, which is described
by the following nonlinear ordinary differential equations
dui(t)
dt
[
= −ai(ui(t)) bi(ui(t)) −
n
j=1
]
wijfj(uj(t)) + Ii ,

i = 1, 2, . . . , n,

(1)
where n ≥ 2 is the number of neurons in work, ui(t) denotes the neuron state, ai the
amplification function, bi the self-signal function, W = (wij) the n×n connection weight matrix,
fi the activation function, and Ii the constant external input.
The model (1) was originally suggested in the pioneering work of Cohen and Grossberg [1].
The work model includes a large number of models from neurobiology, evolutionary
theory and population biology([2])