Global Hopf Bifurcation Analysis of a Neuron Network Model with Time Delays
نویسندگان
چکیده
For a two-neuron network with self-connection and time delays, we carry out stability and bifurcation analysis. We establish that a Hopf bifurcation occurs when the total delay passes a sequence of critical values. The stability and direction of the local Hopf bifurcation are determined using the normal form method and center manifold theorem. To show that periodic solutions exist away from the bifurcation points, we establish that local Hopf branches globally extend for arbitrarily large delays. Mathematics Subject Classification (2010): Primary 34C25, 34K18; Secondary
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