Persistence at the onset of spatiotemporal intermittency in coupled map lattices

– We study persistence in coupled circle map lattices at the onset of spatiotemporal intermittency, an onset which marks a continuous transition, in the universality class of directed percolation, to a unique absorbing state. We obtain a local persistence exponent of θl = 1.49± 0.02 at this transition, a value which closely matches values for θl obtained in stochastic models of directed percolation. This result constitutes suggestive evidence for the universality of persistence exponents at the directed percolation transition. Given that many experimental systems are modelled accurately by coupled map lattices, experimental measurements of this persistence exponent may be feasible. The study of extended dynamical systems is relevant to the understanding of many phenomena in condensed matter physics, such as pattern formation and non-equilibrium phase transitions in coupled chemical reactions, charge density waves and Josephson junction arrays [1]. A simple model which captures much of the underlying complexity of these systems is the coupled map lattice, defined as a collection of elements on a lattice which locally exhibit chaotic dynamics, together with a diffusive local coupling between these elements [2]. Coupled map lattices exhibit a remarkable variety of behaviour, ranging from periodic spatio-temporal structure to intermittency and chaos. Spatially extended dynamical systems exhibiting spatio-temporal intermittency possess both laminar and turbulent phases. The laminar phase is characterized by periodic or even weakly chaotic dynamics, while no spatio-temporally regular structure exists in the turbulent regime. Spatio-temporal intermittency refers to the properties of the state which marks the transition between laminar and turbulent phases. A typical spatial pattern arising in spatiotemporal intermittency consists of fluctuating domains of laminar regions interspersed amidst turbulent ones. Such intermittency is often the precursor of fully developed chaos [2]. An initially laminar site becomes turbulent only if at least one of its neighbours was turbulent at the previous time. A turbulent site can either relax spontaneously to a laminar (∗) E-mail:[email protected] (∗∗) E-mail:[email protected] (∗∗∗) E-mail:[email protected]