CHAOS IN SPATIALLY EXTENDED SYSTEMS VIA THE PEAK-CROSSING BIFURCATION

Abstract

Individual sites in spatially extended systems of coupled identical maps may exhibit chaotic behavior even if their intrinsic (local) dynamics is regular and stable. For this to happen it is imperative that the spatial interactions are sufficiently strong. So far, this scenario of generating chaos from simple local dynamics has been established rigorously only for special, very narrow classes of local maps. The present article largely extends previous results by showing that the corresponding mechanism of peak-crossing is in fact very general and robust: whenever the local map is sufficiently expanding and exhibits a horseshoe then the emergence of spatial intermittency will be observed in the form of chaotically oscillating sites surrounded by quasi-regular clusters. The results firmly establish peak-crossing as a natural scenario on the route to spacetime chaos.