The Feigenbaum's $\delta$ for a high dissipative bouncing ball model

TL;DR

This paper investigates the Feigenbaum's delta in a highly dissipative bouncing ball model, revealing period doubling routes to chaos in a nonlinear, area-contracting map with inelastic collisions.

Contribution

It introduces a high dissipation regime in a bouncing ball model and computes the Feigenbaum's delta, demonstrating a route to chaos via period doubling.

Findings

Identification of period doubling route to chaos

Calculation of Feigenbaum's delta in the model

High dissipation influences bifurcation structure

Abstract

We have studied a dissipative version of a one-dimensional Fermi accelerator model. The dynamics of the model is described in terms of a two-dimensional, nonlinear area-contracting map. The dissipation is introduced via innelastic collisions of the particle with the walls and we consider the dynamics in the regime of high dissipation. For such a regime, the model exhibits a route to chaos known as period doubling and we obtain a constant along the bifurcations so called the Feigenbaum's number $\delta$.