Recently, there are quite a few papers discussing delayed dynamical system with time-varying delays.
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Algorithms↗
Biomedical subjects
Tianping Chen
Publications and source records attributed to Tianping Chen.
Robust global exponential stability of Cohen-Grossberg neural networks with time delays.
In this letter, we discuss delayed Cohen-Grossberg neural network models and investigate their global exponential stability of the equilibrium point for the systems. A set of sufficient conditions ensuring robust global exponential convergence of the Cohen-Grossberg neural networks with time delays are given.
Neural Networks, Computer↗
Global convergence of delayed neural network systems.
In this paper, without assuming the boundedness, strict monotonicity and differentiability of the activation functions, we utilize a new Lyapunov function to analyze the global convergence of a class of neural networks models with time delays. A new sufficient condition guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point is derived. This stability criterion imposes constraints on the feedback matrices independently of the delay parameters. The result is compared with some previous works. Furthermore, the condition may be less restrictive in the case that the activation functions are hyperbolic tangent.
Algorithms↗
New conditions on global stability of Cohen-Grossberg neural networks.
In this letter, we discuss the dynamics of the Cohen-Grossberg neural networks. We provide a new and relaxed set of sufficient conditions for the Cohen-Grossberg networks to be absolutely stable and exponentially stable globally. We also provide an estimate of the rate of convergence.
Neural Networks, Computer↗
Universal approximation of multiple nonlinear operators by neural networks.
Recently, there has been interest in the observed capabilities of some classes of neural networks with fixed weights to model multiple nonlinear dynamical systems. While this property has been observed in simulations, open questions exist as to how this property can arise. In this article, we propose a theory that provides a possible mechanism by which this multiple modeling phenomenon can occur.
Neural Networks, Computer↗
Global convergence rate of recurrently connected neural networks.
We discuss recurrently connected neural networks, investigating their global exponential stability (GES). Some sufficient conditions for a class of recurrent neural networks belonging to GES are given. Sharp convergence rate is given too.
Journal Article↗
A unified algorithm for principal and minor components extraction.
Principal component and minor component extractions provide powerful techniques in many information-processing fields. However, by conventional algorithms minor component extraction is much more difficult than principal component extraction. A unified algorithm which can be used to extract both principal and minor component eigenvectors is proposed. This 'unified' algorithm can extract true principle components (eigenvectors) and if altered simply by the sign, it can also serve as a true minor components extractor. This is of practical significance in neural network implementation. It is shown how the present algorithms are related to Oja's principal subspace algorithm, Xu's algorithm and the Brockett flow. It is also shown that the algorithms are based on the natural gradient ascend/descent methods (a potential flow in a Riemannian space).
Journal Article↗
A unified approach for neural network-like approximation of non-linear functionals.
In this paper, we give a universal approach to approximation of non-linear functionals and so called myopic input-output maps by neural network-like architectures. Strong theorems on equi-uniform approximation to functionals in abstract spaces are given. As applications, theorems on identification of non-linear systems, whose inputs belong to compact sets in C(R(q),R(p)), are given. It is pointed out that: (1) the weighted approximation can be reduced to non-weighted approximation; (2) the continuous case and discrete case can be dealt with universally.
Journal Article↗