Stability, bifurcation, and synchronization of delay-coupled ring neural networks
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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.
KeywordsTime delay Coupled systems Neural networks Synchronization Nonlinear dynamics
The authors thank the financial support from the National Natural Science Foundation of China under Grant Nos. 11472097 and 11002047, the State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and Astronautics) under Grant No. MCMS-0113G01, and the Fundamental Research Funds for the Central Universities under Grant No. 2015B18214. They thank the anonymous reviewers for their helpful comments and suggestions that have helped to improve the presentation of this paper.
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