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

Abstract

We study spatio-temporal 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 behaviour belongs to the DP class. The regimes of non-DP behaviour show spatial intermittency (SI), where the temporal behaviour of both the laminar and burst regions is regular, and the distribution of laminar lengths scales as a power law.The regular temporal behaviour for the bursts seen in these regimes of spatial intermittency can be periodic or quasi-periodic, but the laminar length distributions scale with the same power-law, which is distinct from the DP case. STI with traveling wave (TW) laminar states also appears in the phase diagram. Soliton-like structures appear in this regime. These are responsible for cross-overs with accompanying non-universal exponents. The soliton lifetime distributions show power law scaling in regimes of long average soliton life-times, but peak at characteristic scales with a power-law tail in regimes of short average soliton life-times. The signatures of each type of intermittent behaviour can be found in the dynamical characterisers of the system viz. the eigenvalues of the stability matrix. We discuss the implications of our results for behaviour seen in other systems which exhibit spatio-temporal intermittency.

Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions

“…This was attributed to frequency entrainment at large coupling strengths, which ensured that the frozen phase patterns on the lattice oscillate with a common frequency. Mapping discrete dynamical systems to statistical mechanics models gives new insights into the behavior of these systems [41,42]. The repulsively coupled Kuramoto oscillators serve as a good paradigm in which techniques and ideas related to statistical mechanics can be applied to an inherently dynamical system.…”

Probabilistic signatures of spatiotemporal intermittency in the coupled sine circle map lattice

“…In regimes of long average soliton lifetimes, the distribution of soliton lifetimes shows a power-law behaviour whereas the distribution shows a peak with a characteristic time-scale (∼ 20) in regimes of short soliton lifetimes. These varying average soliton lifetimes influence the extent of spreading in the lattice and therefore lead to varying values for the laminar length distribution exponents [6]. Thus, the creation, propagation, and annihilation of solitons lead to significant changes in the statistical and dynamical behaviour of the system.…”

“…This kind of spatiotemporal intermittency contains coherent structures or 'solitons', which spoil the analogy with directed percolation and are responsible for non-universal exponents in this region [6]. In this paper, we show that a cellular automaton can be designed for this type of spatiotemporal intermittency, which successfully picks up signatures of the 'solitons'.…”

“…In addition to modelocked and synchronised behaviour, the model exhibits a rich variety of phenomena such as spatiotemporal intermittency of the directed percolation class [4,5], spatial intermittency, cluster solutions and regimes with long-lived coherent structures, also known as solitons [6].…”

Dynamical Regularization in Scalefree-Trees of Coupled 2D Chaotic Maps

“…Coupled Maps Systems (CMS) are networks of interacting dynamical systems (maps) that can be easily computationally modeled allowing the study of complex phenomena like synchronization, self-organization or phase transitions [4,5,6,7]. The emergent behavior of a CMS can be investigated in relation to the architecture/topology of the network, type/strength of the coupling or the properties of the uncoupled units, often representing a model of applicational interest [8,9].…”