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DYNAMICS IN TIME-DELAY RECURRENTLY COUPLED OSCILLATORS

CAN JIANG

College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, P. R. China

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SHANGJIANG GUO

College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, P. R. China

Author for correspondence.

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YIGANG HE

College of Electric and Information Engineering, Hunan University, Changsha, Hunan 410082, P. R. China

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https://doi.org/10.1142/S0218127411028787Cited by:3 (Source: Crossref)

Abstract

A model of time-delay recurrently coupled spatially segregated neural oscillators is proposed. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. Bifurcation analysis shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multi-stability, hysteresis, and stability switches of the rest state provoked by the time delay as well as the strength of the connections between the oscillators. Then we derive the equation describing the flow on the center manifold that enables us to determine the bifurcation direction and stability of bifurcated periodic solutions and equilibria. We also give some numerical simulations to support our main results.

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