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
Analysis of continuous attractors for 2-D linear threshold 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
Nontrivial global attractors in 2-D multistable attractor 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
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
IEEE Transactions on Neural Networks
Invariant set of weight of perceptron trained by perceptron training algorithm
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Multistability of delayed neural networks with discontinuous activations
ISNN'10 Proceedings of the 7th 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 multiperiodicity and attractivity for a class of recurrent neural networks (RNNs) with unsaturating piecewise linear transfer functions and variable delays. Using local inhibition, conditions for boundedness and global attractivity are established. These conditions allow coexistence of stable and unstable trajectories. Moreover, multiperiodicity of the network is investigated by using local invariant sets. It shows that under some interesting conditions, there exists one periodic trajectory in each invariant set which exponentially attracts all trajectories in that region correspondingly. Simulations are carried out to illustrate the theories.