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Hopf bifurcation in Cohen-Grossberg neural network with distributed delays. (English) Zbl 1119.34052
The authors of this interesting paper discuss stability and bifurcation of distributed delays Cohen-Grossberg neural networks with two neurons. By choosing the average delay as a bifurcation parameter, they prove that Hopf bifurcation occurs. They also determine the stability of bifurcating periodic solutions and the direction of Hopf bifurcation by applying normal form theory and the center manifold theorem. To support their theoretical predictions, the authors include some numerical simulation results.
MSC:
34K18Bifurcation theory of functional differential equations
92B20General theory of neural networks (mathematical biology)
34K60Qualitative investigation and simulation of models
34K20Stability theory of functional-differential equations