VISUALIZATION OF CORRELATION CASCADE IN SPATIOTEMPORAL CHAOS USING WAVELETS

Abstract

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