Dynamic characterisers of spatiotemporal intermittency

Abstract

We study spatiotemporal intermittency in a system of coupled sine circle maps. The phase diagram of the system shows parameter regimes where the STI lies in the directed percolation class, as well as regimes which show pure spatial intermittency (where the temporal behaviour is regular) which do not belong to the DP class. Thus, both DP and non-DP behaviour can be seen in the same system. The signature of DP and non-DP behaviour can be seen in the dynamic characterisers, viz. the spectrum of eigenvalues of the linear stability matrix of the evolution equation, as well as in the multifractal spectrum of the eigenvalue distribution. The eigenvalue spectrum of the system in the DP regimes is continuous, whereas it shows evidence of level repulsion in the form of gaps in the spectrum in the non-DP regime. The multifractal spectrum of the eigenvalue distribution also shows the signature of DP and non-DP behaviour. These results have implications for the manner in which correlations build up in extended systems.