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Synchronization for two coupled oscillators with inhibitory connection
Author(s) -
Xiao Ke,
Guo Shangjiang
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1225
Subject(s) - mathematics , center manifold , bifurcation , synchronization (alternating current) , hopf bifurcation , connection (principal bundle) , control theory (sociology) , inhibitory postsynaptic potential , biological applications of bifurcation theory , saddle node bifurcation , stability (learning theory) , topology (electrical circuits) , mathematical analysis , nonlinear system , computer science , physics , geometry , combinatorics , neuroscience , artificial intelligence , control (management) , quantum mechanics , machine learning , biology
In this paper we present an oscillatory neural network composed of two coupled neural oscillators with inhibitory connections. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. Regarding time delays τ as the bifurcation parameter, we not only obtain the existence of Hopf bifurcations but also investigate the bifurcation direction and stability of bifurcated periodic solutions by employing normal form theory and center manifold reduction. Finally, numerical simulations are provided to illustrate the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.