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Necessary conditions for complete synchronization of a coupled chaotic Aihara neuron network with electrical synapses. (English) Zbl 1418.92008

Summary: In this paper, the synchronization problem of a chaotic Aihara neuron network is considered. Based on the master stability function (MSF) analysis, some necessary conditions are proposed to investigate the complete synchronization of the electrical coupled chaotic Aihara neuron networks. Especially, the two-dimensional parameter-space plots are obtained numerically to visualize the possible synchronized region. For the chaotic Rulkov neuron network, the numerical simulations of the MSF show that complete synchronization of the electrical coupled Aihara neuron network can be achieved when the coupling strength lies in a suitable interval, while it is highly improbable to attain complete synchronization when all neurons are in the chaotic bursting. Moreover, the complete synchronization cannot be reached with further increase or decrease of coupling strength. These results are probably common features as far as discrete-time neuron networks are concerned. Finally, based on the drive-response active control method, an LMI-based criterion is obtained to ensure complete synchronization of the available chaotic Aihara neuron network. The spatiotemporal patterns measured by the state distribution of neurons are employed to validate the effectiveness of our control scheme.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
92C20 Neural biology
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
93B52 Feedback control
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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