Frustration, stability, and delay-induced oscillations in a neural network model
SIAM Journal on Applied Mathematics
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Global Hopf-bifurcation in a neural netlet
Applied Mathematics and Computation
Global attractivity in delayed Hopfield neural network models
SIAM Journal on Applied Mathematics
On the stability analysis of delayed neural networks systems
Neural Networks
Learning state space trajectories in recurrent neural networks
Neural Computation
A learning algorithm for continually running fully recurrent neural networks
Neural Computation
Distributed delays stabilize neural feedback systems
Biological Cybernetics
Stability switches and bifurcation analysis of a neural network with continuously delay
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Synchronization and stable phase-locking in a network of neurons with memory
Mathematical and Computer Modelling: An International Journal
Stability and Hopf Bifurcation in a Simplified BAM Neural Network With Two Time Delays
IEEE Transactions on Neural Networks
How delays affect neural dynamics and learning
IEEE Transactions on Neural Networks
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In this paper we consider an unidirectional ring of n neurons with distributed delays. The effects of the delay, the coupling strengths and the network size on the stability of the system are investigated. Taking the average delay as a bifurcation parameter, we find two critical values depending on the network size and the coupling strengths, at which the system undergoes Hopf bifurcations. By using the method of multiple scales, we can show that these Hopf bifurcating periodic solutions are asymptotically stable. Finally, the theoretical results are illustrated by numerical simulations for the neural networks with three or four neurons.