Experimental Investigation of Spatial Pattern Formation in Physical Systems of Activator Inhibitor Type

Abstract

We investigate experimentally stationary stable states of activator (w) inhibitor (υ) type systems corresponding to the reaction diffusion equation δ · υ̇ = Δυ + w - υ; ẇ = σ Δw + f(w) - υ; δ, σ = const > 0 with f(w) monotonically increasing for small and decreasing for large |w|. We first describe some general mathematical properties and present qualitative results obtained from numerical calculations. We then investigate experimentally electrical networks described by the spatially discretized version of the above equation. Calculation and experiment are in good agreement. We also interprete a two dimensional-network as an equivalent circuit for a composite material consisting of a linear and a nonlinear layer with an s-shaped current density electric field characteristic. This model is used for a phenomenological description of spatial structures and global current voltage characteristics observed experimentally in pin-diode like and gas discharge devices. The model accounts very well for the experimental results obtained so far. It is concluded that the above equation and the corresponding experimental setup are of great interest for fundamental investigations of self con­trolled processes in nature.