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3. Exponential stability of impulsive high-order Hopfield-type neural networks with time-varying delays

Author

Liu, Xinzhi, Teo, Kok Lay, and Xu, Bingji

Subjects
Neural networks -- Research, Liapunov functions -- Usage, Neural network, Business, Computers, Electronics, Electronics and electrical industries
Abstract

This paper considers the problems of global exponential stability and exponential convergence rate for impulsive high-order Hopfield-type neural networks with time-varying delays. By using the method of Lyapunov functions, some sufficient conditions for ensuring global exponential stability of these networks are derived, and the estimated exponential convergence rate is also obtained. As an illustration, an numerical example is worked out using the results obtained. Index Terms--Exponential stability, impulsive high-order Hopfield-type Lyapunov function, neural networks.

Published
2005

4. Chen 混沌系统全局指数吸引集和正向不变集的构造性证明及应用

Author

Liao Xiao-xin, Yu Pei, XU BingJi, and Chen Guan-Rong

Subjects
S system, Lyapunov function, Discrete mathematics, General Computer Science, Constructive proof, biology, Chaotic, Invariant (physics), biology.organism_classification, Nonlinear Sciences::Chaotic Dynamics, symbols.namesake, Chen, Exponential growth, Chaotic systems, ComputerSystemsOrganization_MISCELLANEOUS, symbols, Applied mathematics, Engineering (miscellaneous), Mathematics
Abstract

In this paper, a constructive proof of the globally exponentially attractive and positively invariant set for the chaotic Chen's system is given, by using several generalized positive de nite Lyapunov functions. The problem of the existence of a globally exponentially attractive set for the chaotic Chen's system is completely solved, which is a long standing open theoretical problem. Methods provided herein can be useful for the study of other forms of chaotic systems.

Published
2015

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