Bifurcation and chaos in one dimensional chains of small particles

TL;DR

This paper investigates bifurcation and chaos in one-dimensional chains of small particles, analyzing systems with fourth- and eighth-order potentials, revealing complex behaviors and Lyapunov exponents.

Contribution

It revisits a known fourth-order potential system with new insights and introduces a novel eighth-order potential system, analyzing their bifurcation and chaotic dynamics.

Findings

Presence of three-armed star behavior in the fourth-order system

Lyapunov exponent analysis of both systems

Distinct bifurcation profiles for the two potentials

Abstract

This work deals with bifurcation and the chaotic behavior in one dimensional chains of small particles. We consider two distinct possibilities, one where the particles are modeled by a fourth-order potential which was already studied. We revisit this system and bring novelties concerning the presence of the three-armed star behavior and the study of the corresponding Lyapunov exponent. The other system is new, and there the particles are more involved and modeled by an eighth-order potential. We investigate this new system within the same approach, emphasizing the behavior of the orbits, the bifurcation profile and the corresponding Lyapunov exponent.