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Multistability and stable asynchronous periodic oscillations in a multiple-delayed neural system. (English) Zbl 1100.34054

Here, neural networks with multiple delays are studied. Local stability and bifurcations of the trivial solution of such systems are analyzed. It is proved that the existence of standard Hopf bifurcations gives rise to synchronized periodic solutions, as well as \(D_3\) equivariant Hopf bifurcations give rise to phase-locked, mirror-reflecting and standing waves.

MSC:

34K13 Periodic solutions to functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional-differential equations
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