Abstract
In this thesis, we mainly discuss the existence of the traveling wave solutions for reaction-diffusion type partial difference systems. In particular, we pay attention to the following four models:(1) reaction-diffusion equation with linear diffusion and linear reaction term,(2) reaction-diffusion equation with linear diffusion and polynomial reaction term,(3) discretization of λ-ω system, and(4) discretization of RTD-based cellular neural networks.For models (1), (2) and (3), we consider their “periodic traveling wave” solutions; and for model (4), we consider its “traveling wave front” solutions.The existence criteria for these solutions are established by means of spectral properties of circulant matrices, an implicit function theorem, monotone iteration method and basic analysis. In addition, examples are also given to illustrate of our results.