Journal ArticleDOI
Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays
TLDR
The authors analyze the existence of the equilibrium point and global exponential stability for Hopfield reaction-diffusion neural networks with time-varying delays by means of the topological degree theory and generalized Halanay inequality.Abstract:
The authors analyze the existence of the equilibrium point and global exponential stability for Hopfield reaction-diffusion neural networks with time-varying delays by means of the topological degree theory and generalized Halanay inequality. Since the diffusion phenomena and time delay could not be ignored in neural networks and electric circuits, the model presented here is close to the actual systems, and the sufficient conditions on global exponential stability established in this paper, which are easily verifiable, have a wider adaptive range.read more
Citations
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Journal ArticleDOI
Impulsive delay differential inequality and stability of neural networks
Daoyi Xu,Zhichun Yang +1 more
TL;DR: In this article, a generalized model of neural networks involving time-varying delays and impulses is considered, and sufficient conditions for global exponential stability of impulsive delay model are obtained.
Journal ArticleDOI
Periodic solutions and its exponential stability of reaction–diffusion recurrent neural networks with continuously distributed delays
TL;DR: In this article, the authors considered both exponential stability and periodic oscillatory solutions for reaction-diffusion recurrent neural networks with continuously distributed delays and provided sufficient conditions to ensure global exponential stability.
Journal ArticleDOI
Global exponential robust stability of reaction¿diffusion interval neural networks with time-varying delays
TL;DR: In this paper, the existence of the equilibrium point and its global exponential robust stability for reaction-diffusion interval neural networks with time-varying delays was discussed by means of the topological degree theory and Lyapunov functional method.
Journal ArticleDOI
Delay-dependent robust exponential stability of Markovian jumping reaction-diffusion Cohen–Grossberg neural networks with mixed delays
TL;DR: Some criteria for delay-dependent robust exponential stability of RDCGNNs with Markovian jumping parameters are established in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing Matlab LMI toolbox.
Journal ArticleDOI
Stochastic exponential stability of the delayed reaction–diffusion recurrent neural networks with Markovian jumping parameters
TL;DR: In this paper, some criteria for the global stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters are presented, and the criteria are computationally efficient, since they are in the forms of some linear matrix inequalities.
References
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Journal ArticleDOI
Neurons with graded response have collective computational properties like those of two-state neurons.
TL;DR: A model for a large network of "neurons" with a graded response (or sigmoid input-output relation) is studied and collective properties in very close correspondence with the earlier stochastic model based on McCulloch - Pitts neurons are studied.
Book
Neurons with graded response have collective computational properties like those of two-state neurons
TL;DR: In this article, a model for a large network of "neurons" with a graded response (or sigmoid input-output relation) is studied, which has collective properties in very close correspondence with the earlier stochastic model based on McCulloch--Pitts neurons.
Journal ArticleDOI
Computing with neural circuits: a model
TL;DR: A new conceptual framework and a minimization principle together provide an understanding of computation in model neural circuits that represent an approximation to biological neurons in which a simplified set of important computational properties is retained.
Book
Theory and Applications of Partial Functional Differential Equations
TL;DR: In this paper, the existence and compactness of solution semiflows of linear systems are investigated. But the authors focus on the nonhomogeneous systems and do not consider the linearized stability of non-homogeneous solutions.
Journal ArticleDOI
Neural networks for nonlinear programming
TL;DR: In this paper, the dynamics of the modified canonical nonlinear programming circuit are studied and how to guarantee the stability of the network's solution, by considering the total cocontent function.
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