Bounds on nonlinear operators in finite-dimensional banach spaces
Numerische Mathematik
On the stability of globally projected dynamical systems
Journal of Optimization Theory and Applications
New theorems on global convergence of some dynamical systems
Neural Networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A reference model approach to stability analysis of neural networks
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
On equilibria, stability, and instability of Hopfield neural networks
IEEE Transactions on Neural Networks
Stability of asymmetric Hopfield networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
Global convergence of delayed dynamical systems
IEEE Transactions on Neural Networks
Robust global exponential stability of Cohen-Grossberg neural networks with time delays
IEEE Transactions on Neural Networks
Solving Quadratic Programming Problems by Delayed Projection Neural Network
IEEE Transactions on Neural Networks
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Critical dynamics research of recurrent neural networks (RNNs) is very meaningful in both theoretical importance and practical significance. Due to the essential difficulty in analysis, there were only a few contributions concerning it. In this paper, we devote to study the critical dynamics behaviors for RNNs with general forms. By exploring some intrinsic features processed naturally by the nonlinear activation mappings of RNNs, and by using matrix measure theory, new criteria are found to ascertain the globally exponential stability of RNNs under the critical conditions. The results obtained here either yield new, or sharpen, extend or unify, to a large extent, most of the existing non-critical conclusions as well as the latest critical results.