Visualization of correlation cascade in spatio-temporal chaos using wavelets

Abstract

We propose a simple method to visualize spatio-temporal correlation between scales using wavelets, and apply it to two typical spatio-temporally chaotic systems, namely to coupled complex Ginzburg-Landau oscillators with diffusive interaction, and those with non-local interaction. Reflecting the difference between underlying dynamical processes, our method provides distinctive results for those two systems. Especially, for the non-locally interacting case where the system exhibits fractal amplitude patterns and power-law spectrum, it clearly visualizes the dynamical cascade process of spatio-temporal correlation between scales.