A Winner-Take-All Neural Networks of N Linear Threshold Neurons without Self-Excitatory Connections
Neural Processing Letters
Multistability of Neural Networks with a Class of Activation Functions
ISNN '09 Proceedings of the 6th International Symposium on Neural Networks on Advances in Neural Networks
Discrete-time recurrent neural networks with complex-valued linear threshold neurons
IEEE Transactions on Circuits and Systems II: Express Briefs
Representations of continuous attractors of recurrent neural networks
IEEE Transactions on Neural Networks
Permitted and forbidden sets in discrete-time linear threshold recurrent neural networks
IEEE Transactions on Neural Networks
Solving the CLM Problem by Discrete-Time Linear Threshold Recurrent Neural Networks
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
Delayed neural networks with multistable almost periodic solutions
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Multistability and new attraction basins of almost-periodic solutions of delayed neural networks
IEEE Transactions on Neural Networks
Foundations of implementing the competitive layer model by Lotka-Volterra recurrent neural networks
IEEE Transactions on Neural Networks
Multistability in networks with self-excitation and high-order synaptic connectivity
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Identification of finite state automata with a class of recurrent neural networks
IEEE Transactions on Neural Networks
IEEE Transactions on Neural Networks
ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
A Competitive Layer Model for Cellular Neural Networks
Neural Networks
Stability analysis of multiple equilibria for recurrent neural networks
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
| Hi-index | 0.00 |
This paper studies the multistability of a class of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions. It addresses the nondivergence, global attractivity, and complete stability of the networks. Using the local inhibition, conditions for nondivergence are derived, which not only guarantee nondivergence, but also allow for the existence of multiequilibrium points. Under these nondivergence conditions, global attractive compact sets are obtained. Complete stability is studied via constructing novel energy functions and using the well-known Cauchy Convergence Principle. Examples and simulation results are used to illustrate the theory.