Dynamic characterizers of spatiotemporal intermittency

Abstract

Systems of coupled sine circle maps show regimes of spatiotemporally intermittent behaviour with associated scaling exponents which belong to the DP class, as well as regimes of spatially intermittent behaviour (with associated regular dynamical behaviour) which do not belong to the DP class. Both types of behaviour are seen along the bifurcation boundaries of the synchronized solutions, and contribute distinct signatures to the dynamical characterizers of the system, viz. the distribution of eigenvalues of the one step stability matrix. Within the spatially intermittent (SI) class, the temporal behaviour of the burst solutions can be quasi-periodic or travelling wave. The usual characterizers of bifurcations, i.e. the eigenvalues of the stability matrix crossing the unit circle, pick up the bifurcation from the synchronized solution to SI with quasi-periodic bursts but are unable to pick up the bifurcation of the synchronized solution to SI with TW bursts. Other characterizers, such as the Shannon entropy of the eigenvalue distribution, and the rate of change of the largest eigenvalue with parameter are required to pick up this bifurcation. This feature has also been seen for other bifurcations in this system, e.g. that from the synchronized solution to kink solutions. We therefore conjecture that in the case of high dimensional systems, entropic characterizers provide better signatures of bifurcations from one ordered solution to another.