Nonlinear Waves in Networks of Neurons with Delayed Feedback: Pattern Formation and Continuation
Lihong Huang, Jianhong Wu · SIAM Journal on Mathematical Analysis · 2003
An on-center off-surround network of three identical neurons with delayed feedback is considered, and the effect of synaptic delay of signal transmission on the pattern formation and global continuation of nonlinear waves is described. The spontaneous bifurcation of multiple branches of periodic solutions is discussed, and their spatio-temporal patterns and mode interactions are studied by using the symmetric bifurcation theory of delay differential equations coupled with representation theory of standard dihedral groups, Liapunov's direct method, LaSalle's invariance principle, a priori estimates, and differential inequalities.