Nonlinear waves in networks of neurons with delayed feedback: Pattern formation and continuation. (English) Zbl 1038.34076

Huang, Lihong; Wu, Jianhong

SIAM J. Math. Anal. 34, No. 4, 836-860 (2003).

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.

Reviewer: Angela Slavova (Sofia)

MSC:

34K18	Bifurcation theory of functional-differential equations
34K20	Stability theory of functional-differential equations
34C25	Periodic solutions to ordinary differential equations
92B20	Neural networks for/in biological studies, artificial life and related topics

Keywords:

wave; neural network; delay; bifurcation; global continuation