Controlled diffusion processes in an adiabatic model of a bouncing ball

TL;DR

This paper investigates how adding a diffusion control parameter to a chaotic bouncing ball model influences its dynamics, revealing complex interactions between deterministic chaos and stochastic diffusion.

Contribution

It introduces a novel diffusion-controlled extension to the bouncing ball model, bridging chaotic dynamics with stochastic diffusion effects.

Findings

Diffusion control alters the chaotic behavior of the bouncing ball.

The model shows complex dynamics arising from chaos and diffusion interaction.

Reinterprets collisions as thermal fluctuations, linking to particle behavior.

Abstract

This study explores the integration of a diffusion control parameter into the chaotic dynamics of a modified bouncing ball model. By extending beyond simple elastic collisions, the model introduces elements that affect the diffusive behavior of kinetic energy, offering insights into the interplay between deterministic chaos and stochastic diffusion. The research reinterprets the bouncing ball's interactions with the surface as short-distance collisions that mimic random thermal fluctuations of particles. This refined model reveals complex dynamics, highlighting the synergistic effects between chaos and diffusion in shaping the evolution of the system.