Chaotic dynamics of a three particle array under Lennard--Jones type forces and a fixed area constraint

TL;DR

This paper investigates the chaotic behavior of a three-particle system under Lennard-Jones forces with a fixed area constraint, using numerical methods and a novel chaos measure to analyze stability.

Contribution

It introduces a numerical study of chaos in a constrained three-particle Lennard-Jones system using a new chaos measure by Hunt and Ott.

Findings

Evidence of chaotic dynamics under certain conditions

Numerical stability analysis of the system

Application of Hunt and Ott's chaos measure

Abstract

We consider the dynamical problem for a system of three particles in which the inter-particle forces are given as the gradient of a Lennard-Jones type potential. Furthermore we assume that the three particle array is subject to the constraint of fixed area. The corresponding mathematical problem is that of a conservative dynamical system over the manifold determined by the area constraint. We study numerically the stability of this system. In particular, using the recently introduced measure of chaos by Hunt and Ott (2015), we study numerically the possibility of chaotic behavior for this system.