A cellular automaton identification of the universality classes of spatiotemporal intermittency

TL;DR

This paper investigates the universality classes of spatiotemporal intermittency in coupled sine circle map lattices, revealing a transition from probabilistic to deterministic cellular automata that signals different universality classes.

Contribution

It introduces a cellular automaton framework to distinguish universality classes of intermittency and identifies a transition from probabilistic to deterministic automata at the infection line.

Findings

Identification of two distinct types of spatio-temporal intermittency.

Mapping of the coupled map lattice to a cellular automaton.

Transition from probabilistic to deterministic automaton at the infection line.

Abstract

The phase diagram of the coupled sine circle map lattice shows spatio-temporal intermittency of two distinct types: spatio-temporal intermittency of the directed percolation (DP) class, and spatial intermittency which does not belong to this class. These two types of behaviour are seen to be special cases of the spreading and non-spreading regimes seen in the system. In the spreading regime, each site can infect its neighbours permitting an initial disturbance to spread, whereas in the non-spreading regime no infection is possible. The two regimes are separated by a line which we call 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 (PCA) to a deterministic cellular automaton (DCA) at the infection line. Thus the existence of the DP and non-DP universality classes in the same system is signalled by the PCA to DCA transition. We also discuss the dynamic origin of this transition.