Spatiotemporal intermittency and scaling laws in the coupled sine circle map lattice

Abstract

We study spatiotemporal intermittency (STI) in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes with STI of both the directed percolation (DP) and non-DP class. STI with synchronized laminar behavior belongs to the DP class. The regimes of non-DP behavior show spatial intermittency (SI), where the temporal behavior of both the laminar and burst regions is regular, and the distribution of laminar lengths scales as a power law. The regular temporal behavior for the bursts seen in these regimes of spatial intermittency can be periodic or quasiperiodic, but the laminar length distributions scale with the same power law, which is distinct from the DP case. STI with traveling wave laminar states also appears in the phase diagram. Solitonlike structures appear in this regime. These are responsible for crossovers with accompanying nonuniversal exponents. The soliton lifetime distributions show power-law scaling in regimes of long average soliton lifetimes, but peak at characteristic scales with a power-law tail in regimes of short average soliton lifetimes. The signatures of each type of intermittent behavior can be found in the dynamical characterizers of the system viz. the eigenvalues of the stability matrix. We discuss the implications of our results for behavior seen in other systems which exhibit spatiotemporal intermittency.