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Stability, bifurcation, and synchronization of delay-coupled ring neural networks. (English) Zbl 1354.93133
Summary: This paper studies the nonlinear dynamics of coupled ring networks each with an arbitrary number of neurons. Different types of time delays are introduced into the internal connections and couplings. Local and global asymptotical stability of the coupled system is discussed, and sufficient conditions for the existence of different bifurcated oscillations are given. Numerical simulations are performed to validate the theoretical results, and interesting neuronal activities are observed, such as rest state, synchronous oscillations, asynchronous oscillations, and multiple switches of the rest states and different oscillations. It is shown that the number of neurons in the sub-networks plays an important role in the network characteristics.

MSC:
93D20 Asymptotic stability in control theory
34D06 Synchronization of solutions to ordinary differential equations
34B45 Boundary value problems on graphs and networks for ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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