Inducing periodicity in lattices of chaotic maps with advection

TL;DR

This paper explores how adding advection to a lattice of chaotic logistic maps induces periodic behavior and complex wave phenomena, analyzed through Lyapunov exponents and spatial inhomogeneity effects.

Contribution

It introduces a novel approach of incorporating advection into coupled logistic maps, revealing new dynamics and intermittent wave phenomena not seen in purely diffusive systems.

Findings

Advection induces periodicity in chaotic lattice maps.

Spatial inhomogeneity leads to intermittent wave-like pulses.

Lyapunov exponents characterize the system's stability and behavior.

Abstract

We investigate a lattice of coupled logistic maps where, in addition to the usual diffusive coupling, an advection term parameterized by an asymmetry in the coupling is introduced. The advection term induces periodic behavior on a significant number of non-periodic solutions of the purely diffusive case. Our results are based on the characteristic exponents for such systems, namely the mean Lyapunov exponent and the co-moving Lyapunov exponent. In addition, we study how to deal with more complex phenomena in which the advective velocity may vary from site to site. In particular, we observe wave-like pulses to appear and disappear intermittently whenever the advection is spatially inhomogeneous.