DYNAMICS OF DISSIPATIVE STRUCTURES IN REACTION-DIFFUSION EQUATIONS

The authors investigate the dynamics of dissipative structures in a re action-diffusion system. They propose an analytical theory for the beh avior of dissipative structures and show that a dissipative structure (DS) that is stable in a one-dimensional homogeneous medium can be ind uced to drift by slow variation of the diffusion coefficients, or by c urvature of the DS in higher dimensions. In one spatial dimension, thi s motion can be in the direction of increasing or decreasing diffusion coefficient, depending on properties of the DS which can be determine d analytically. In two and three dimensions this drift is proportional to the sum of the curvature of the DS and the gradient of the diffusi on coefficient of the medium. The analysis of this motion uses standar d ideas from perturbation theory to find an equation of motion for the location of the DS. Numerical simulations in one and two dimensions s how good quantitative agreement with the theoretical results.