Convergent activation dynamics in continuous time networks
Neural Networks
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Chaos and Synchronization of Time-Delayed Fractional Neuron Network System
ICYCS '08 Proceedings of the 2008 The 9th International Conference for Young Computer Scientists
Dynamics of a discrete-time bidirectional ring of neurons with delay
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Fractional-order hopfield neural networks
ICONIP'08 Proceedings of the 15th international conference on Advances in neuro-information processing - Volume Part I
How delays affect neural dynamics and learning
IEEE Transactions on Neural Networks
Projective synchronization for fractional neural networks
Neural Networks
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Several topics related to the dynamics of fractional-order neural networks of Hopfield type are investigated, such as stability and multi-stability (coexistence of several different stable states), bifurcations and chaos. The stability domain of a steady state is completely characterized with respect to some characteristic parameters of the system, in the case of a neural network with ring or hub structure. These simplified connectivity structures play an important role in characterizing the network's dynamical behavior, allowing us to gain insight into the mechanisms underlying the behavior of recurrent networks. Based on the stability analysis, we are able to identify the critical values of the fractional order for which Hopf bifurcations may occur. Simulation results are presented to illustrate the theoretical findings and to show potential routes towards the onset of chaotic behavior when the fractional order of the system increases.