Difference Approximations of a Reaction–Diffusion Equation on Segments

Abstract

The system of phase differences for a chain of diffuse weakly coupled oscillators on a stable integral manifold is constructed and analyzed. It is shown (by means of numerical methods) that Lyapunov dimension growth is close to linear as the number of oscillators in the chain increases. Extensive computations performed for the difference model of the Ginsburg–Landau equation illustrate this result and determine the applicability limits for asymptotic methods.