Structure of synchronized chaos studied by symbolic analysis in velocity-curvature space

TL;DR

This paper introduces a symbolic analysis method based on velocity-curvature space to study synchronized chaos, revealing attractor structure changes in coupled logistic maps.

Contribution

A novel symbolic analysis technique using velocity-curvature space is proposed for analyzing discrete dynamical systems and synchronization phenomena.

Findings

Method effectively reveals attractor structure changes.

Applied to coupled logistic maps, it detects synchronization escape.

Demonstrates utility in studying synchronized chaos.

Abstract

A new method of symbolic analysis based on finite discretization of velocity-curvature space is proposed. A minimum alphabet is introduced in a natural way, and a number of initial analytic measures are defined that make it possible to study the structure of discrete mapping dynamics. The proposed method is tested by application to a system of two unidirectionally coupled logistic maps. It is shown that this method can be used to reveal and study changes in the structure of attractors. In the given example, features in the attractor structure of the driven subsystem are studied upon its escape from the identical synchronization regime.