# The velocity of dynamical chaos during propagation of the positive Lyapunov exponents region under non-local conditions

## TL;DR

This paper investigates how chaos propagates in systems with mixed regular and chaotic regions, analyzing the velocity of chaos spread through classical and non-local heat transfer models under different disturbances.

## Contribution

It introduces a study of chaos propagation velocity in systems with non-local interactions and initial mixed dynamics, expanding understanding of non-stationary heat transfer behavior.

## Key findings

- Chaos propagates with measurable velocity in both classical and non-local models.
- System response varies significantly with different initial disturbances.
- The maximal Lyapunov exponent region's movement characterizes chaos spread.

## Abstract

The dynamics of the system is investigated when one part of the system initially behaves in a regular manner and the other in a chaotic one. The propagation of the chaos is considered as the motion of a region with the maximal Lyapunov exponent greater than zero. The time dependencies of the chaos propagation parameters were calculated for the classical and non-local models of non-stationary heat transfer. The system responses were considered to disturbances in the form of the Dirac delta function and the Heaviside step function.