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Stability and Hopf bifurcation analysis on a four-neuron BAM neural network with distributed delays. (English) Zbl 1221.37198

Summary: A four-neuron BAM neural network with distributed delays is considered, where kernels are chosen as weak kernels. Its dynamics is studied in terms of local stability analysis and Hopf bifurcation analysis. By choosing the average delay as a bifurcation parameter and analyzing the associated characteristic equation, Hopf bifurcation occurs when the bifurcation parameter passes through some exceptive values. The stability of bifurcating periodic solutions and a formula for determining the direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Finally, numerical simulation results are given to validate the theorem obtained.

MSC:

37N25 Dynamical systems in biology
34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K40 Neutral functional-differential equations
92C20 Neural biology
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