This article is cited in 15 papers

Difference approximations of “reaction–diffusion” equation on a segment

S. D. Glyzin

P. G. Demidov Yaroslavl State University

Abstract: The system of phase differences for a chain of diffuse weakly coupled oscillators on a stable integral manifold is constructed and analysed. It is shown by means of numerical methods that as the number of oscillators in the chain increases, the Lyapunov dimention growth is close to linear. The extensive computations performed for difference model of Ginsburg-Landau equation illustrate this result and determine the applicability limits for asymptotic methods.

Keywords: chaotic attractor, autooscillations, autogenerator, Lyapunov's dimension, bifurcations, invariant torus.

UDC: 517.9

Received: 22.09.2009