LOCAL EXISTENCE AND STABILITY OF
PERIODIC TRAVELING WAVES OF
LATTICE FUNCTIONAL DIFFERENTIAL EQUATIONS

XINGFU ZOU AND JIANHONG WU

Dedicated to Professor J. Kato on the occasion of his sixtieth birthday

Abstract. Motivated by a neural network model and a population dynamics model, we consider a discrete Nagumo system with time delay and nonlinear nonlocal interactions. The existence of periodic traveling wave solutions is established by using the symmetric Hopf bifurcation theory recently developed, and the stability of periodic traveling wave solutions under small spatially periodic perturbations is investigated.