Convergence in reaction–diffusion systems: an information theory approach

We have applied an information theory approach in order to study the problem of convergence to point-like or extended attractors in reaction–diffusion systems. A distance between two states based on the Küllback–Leibler relative information was defined. Different forms of the probability distribution, some of them based on the knowledge of the nonequilibrium potential when accesible, give the possibility to look for a faster and/or more accurate convergence. This approach offers the chance to estimate the attraction basins of the different attractors as well as detecting limit circles, together with an easy evaluation of their periods.