Volume 6, Number 4, Winter 1998
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.