A Mexican hat dance: clustering in Ricker-potential particle systems

TL;DR

This paper investigates how particles coupled by the Ricker potential self-organize into complex structures under varying background potentials, revealing rich bifurcation phenomena and diverse dynamical behaviors.

Contribution

It introduces a detailed analysis of particle clustering and bifurcations in Ricker-potential systems under external confinement, highlighting new dynamical patterns.

Findings

Particles form stacks with varying sizes and positions.

Bifurcations lead to diverse self-organized structures.

Rich dynamical behaviors observed under different conditions.

Abstract

The dynamics and spontaneous organization of coupled particles is a classic problem in modeling and applied mathematics. Here we examine the behavior of particles coupled by the Ricker potential, exhibiting finite local repulsion transitioning to distal attraction, leading to an energy-minimizing ``preferred distance''. When compressed by a background potential well of varying severity, these particles exhibit intricate self-organization into ``stacks" with varying sizes and positions. We examine bifurcations of these high-dimensional arrangements, yielding tantalizing glimpses into a rich dynamical zoo of behavior.