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DY: Fachverband Dynamik und Statistische Physik
DY 27: Nonlinear Dynamics, Synchronization and Chaos - Part II
DY 27.7: Vortrag
Donnerstag, 3. April 2014, 11:15–11:30, ZEU 160
Chaotic and statistical properties of two coupled Pomeau-Manneville maps — •Matteo Sala1, Cesar Manchein2, and Roberto Artuso3 — 1MPI PKS, Dynamical systems and Social Dynamics, Nöthnitzer Straße 38, 01187 Dresden, Germany — 2Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil — 3Center for Nonlinear and Complex Systems, Dipartimento di Scienza ed Alta Tecnologia, Via Valleggio 11, 22100 Como, Italia
By considering a 2-D map on the torus defined by two identical Pomeau-Manneville maps interacting through a linear coupling, we study the subtle interplay between intermittency (due to the marginal instability) and synchronization (due to the coupling). In particular, we focus on the weak coupling regime in the range of nonlinearity for which the 1-D Pomeau-Manneville map admits an absolutely continuous invariant measure. Our analysis is based on the phase-space filling rate of non-synchronized orbits and the associated statistics of both the recurrence times and the finite-time Lyapunov exponents. Two main results show up: i) the detection of a clear stretched-exponential trend in both the phase-space filling rate and the decay of rare values probability for the Lyapunov exponent and ii) the coexistence of regular and anomalous behavior in the cumulative probability of recurrence times. These points lead to the conclusion that even a linear, very weak interaction between nonlinear intermittent systems can bring into play extremely non-trivial dynamical features.