Existence and stability of a synchronous oscillation in a neural system with delayed coupling |
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| Authors: | Israel Ncube |
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| Affiliation: | Department of Mathematics, Memorial University of Newfoundland, 20 University Drive, Corner Brook, NL, A2H 5G4, Canada |
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| Abstract: | The article deals with a particular case of a two-neuron network with two discrete time delays. We analyse the linear stability for the particular equilibrium (0,0), and address the Hopf bifurcation which may occur as one of the delays crosses some critical values. The network under consideration has no self-connections, and thus only one time delay appears in the characteristic equation. |
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| Keywords: | Delay differential equations Centre manifold Normal form Hopf bifurcation Existence and uniqueness Criticality |
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