Self-organization in Trees and Motifs of Two-Dimensional Chaotic Maps with Time Delay

Details Self-organization in Trees and Motifs of Two-Dimensional Chaotic Maps with Time Delay Self-organization in Trees and Motifs of Two-Dimensional Chaotic Maps with Time Delay

2007-11-06

arxiv.org/abs/0711.0822v1

Journal of Statistical Mechanics, P03003, 2008

Physics

Condensed Matter

Statistical Mechanics

Submitted to Journal of Statistical Mechanics

Scientific paper

We study two-dimensional chaotic standard maps coupled along the edges of scale-free trees and tree-like subgraph (4-star) with a non-symplectic coupling and time delay between the nodes. Apart from the chaotic and regular 2-periodic motion, the coupled map system exhibits variety of dynamical effects in a wide range of coupling strengths. This includes dynamical localization, emergent periodicity, and appearance of strange non-chaotic attractors. Near the strange attractors we find long-range correlations in the intervals of return-times to specified parts of the phase space. We substantiate the analysis with the finite-time Lyapunov stability. We also give some quantitative evidence of how the small-scale dynamics at 4-star motifs participates in the genesis of the collective behavior at the whole network.

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