UNIVERSAL MULTIFRACTAL STATIONARY DENSITIES IN EXPANDING PIECEWISE LINEAR COUPLED MAPS

Abstract

The phenomenon of synchronization in coupled chaotic maps has been studied extensively by the researchers in nonlinear dynamics for several years. But, there is hardly any study of the stationary densities of coupled maps as a function of the coupling parameter. Here, we numerically analyze stationary densities of two nonlinearly coupled tent maps. In the process, we find that the emergent stationary density can become multifractal even if the stationary density of the individual maps is smooth. In this work, we study piecewise linear and everywhere expanding maps as the stationary density for these maps is described by a simple functional relation. By extensive numerical simulations we find that for this class of maps the multifractal spectrum is universal and does not seem to change with the coupling or map parameters. The existence of this multifractal nature is not surprising, a posteriori, as it is known the densities satisfying similar functional relation are known to be multifractal but the form of the multifractal spectrum here is intriguing as it does not seem to conform to the existing theory of multifractal functions.