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

TL;DR

This paper investigates the time-evolution and regularization process of coupled 2D chaotic maps on a scale-free tree at the stability threshold, revealing unexpected regularities and power-law distributions in the system's steady states.

Contribution

It uncovers novel regularity patterns and statistical properties of the system's steady states at the stability threshold, advancing understanding of chaotic map dynamics on complex networks.

Findings

All period values are integer multiples of specific numbers.

Period distribution follows a power-law with slope -2.24.

Regularization occurs at the stability threshold.

Abstract

The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree is studied, with different types of the collective behaviors already been reported for various values of coupling strength [1]. In this work we focus on the dynamics' time-evolution at the coupling strength of the stability threshold and examine the properties of the regularization process. The time-scales involved in the appearance of the regular state and the periodic state are determined. We find unexpected regularity in the the system's final steady state: all the period values turn out to be integer multiples of one among given numbers. Moreover, the period value distribution follows a power-law with a slope of -2.24.