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A model in a coupled system of simple neural oscillators with delays. (English) Zbl 1176.34087
A coupled system of simple neural oscillators with delays is studied. The authors prove that there is fully symmetric solution which loses stability as a parameter varies, and this loss of stability is due to the crossing of imaginary eigenvalues through the imaginary axis. So, Hopf bifurcation to periodic solutions appears. Moreover, spatio-temporal patterns appear as mirror-reflecting waves, standing waves, etc. which can be seen from the computer simulations.

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