The dynamical origin of the universality classes of spatiotemporal intermittency

Abstract

Studies of the phase diagram of the coupled sine circle map lattice have identified the presence of two distinct universality classes of spatiotemporal intermittency viz. spatiotemporal intermittency of the directed percolation class with a complete set of directed percolation exponents, and spatial intermittency which does not belong to this class. We show that these two types of behavior are special cases of a spreading regime where each site can infect its neighbors permitting an initial disturbance to spread, and a non-spreading regime where no infection is possible, with the two regimes being separated by a line, the infection line. The coupled map lattice can be mapped on to an equivalent cellular automaton which shows a transition from a probabilistic cellular automaton to a deterministic cellular automaton at the infection line. The origins of the spreading-non-spreading transition in the coupled map lattice, as well as the probabilistic to deterministic transition in the cellular automaton lie in a dynamical phenomenon, an attractor-widening crisis at the infection line. Indications of unstable dimension variability are seen in the neighborhood of the infection line. This may provide useful pointers to the spreading behavior seen in other extended systems.