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Nonlinear waves in networks of neurons with delayed feedback: Pattern formation and continuation. (English) Zbl 1038.34076
Here, a network of three identical neurons with delayed feedback is considered. The local bifurcation and the asymptotic forms of the waves are studied. The authors prove that near each critical value ${\tau }_{k}$ there exist eight branches of periodic solutions, two of which are phase-locked, three are standing waves, and three are mirror-reflecting waves. The global continuation of these waves is investigated as well. The spatio-temporal patterns are studied by using the symmetric bifurcation theory of delay differential equations.
##### MSC:
 34K18 Bifurcation theory of functional differential equations 34K20 Stability theory of functional-differential equations 34C25 Periodic solutions of ODE 92B20 General theory of neural networks (mathematical biology)
##### Keywords:
wave; neural network; delay; bifurcation; global continuation