Dynamical topology and statistical properties of spatiotemporal chaos

TL;DR

This paper investigates the statistical properties and dynamics of special topological points in one-dimensional spatiotemporal chaos, providing numerical analysis and a unified probabilistic model for their behavior.

Contribution

It introduces a comprehensive numerical analysis and a unified probabilistic model for the dynamics of topologically special points in spatiotemporal chaos.

Findings

Distribution functions for number, lifespan, and distance of points

Numerical simulations support the probabilistic model

Unified approach applicable across different chaos definitions

Abstract

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In despite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.