Diffusive Lorenz dynamics: Coherent structures and spatiotemporal chaos

Abstract In this paper, we are interested in collective behaviors of many interacting Lorenz strange attractors. With an intermediate diffusion coupling between the attractors, a new remarkable synchronization of well organized structures merges as a result of two competing mechanisms: temporal chaos and spatial diffusive stabilization. A window of the coupling parameter for coherent structures is found numerically. Different from all existing scenarios of routes to chaos (period doubling, intermittency and strange attractors), an algorithmetic increase of wavenumbers before an abrupt change to chaos (compared to the periodic doubling geometrical) is unexpectedly discovered. Meta-stable states axe also observed in simulations.