Spatio-temporal Chaos. 3. Natural Spatio-temporal Measures for Coupled Circle Map Lattices

Spatio-temporal Chaos. 1. Hyperbolicity, Structural Stability, Spatio-temporal Shadowing and Symbolic Dynamics

In a series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are innnite-dimensional analogues of Axiom A systems. Our main result is the existence of a natural spatio-temporal measure which is the spatio-temporal analogue of the SRB measure. In this paper we develop a stable manifold theory for such systems as ...

Spatio-temporal Chaos. 2. Unique Gibbs States for Higher-dimensional Symbolic Systems

In a series of three papers, we study the geometrical and statistical structure of a class of coupled map lattices with natural couplings. These are innnite-dimensional analogues of Axiom A systems. Our main result is the existence of a natural spatio-temporal measure which is the spatio-temporal analogue of the SRB measure. In the rst paper we develop a stable manifold theory for such systems ...

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 percola...

Topological Horseshoe in Travelling Waves of Discretized KdV-Burgers-KS type Equations

Applying the concept of anti-integrable limit to space-time discretized KdV-Burgers-KS type equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions of the resulted coupled map lattices. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.

Assessment of spatio-temporal variations of surface water quality and prioritization of pollution Sources (case Study: Talar Watershed, Mazandaran province)