Complexity Analysis in Bouncing Ball Dynamical System

TL;DR

This paper systematically analyzes the complexity of a bouncing ball system, revealing chaotic behavior through bifurcation diagrams and calculating measures like Lyapunov exponents, entropy, and correlation dimension.

Contribution

It provides a detailed complexity analysis of the nonlinear bouncing ball system using numerical methods and graphical representations, highlighting chaos under specific parameters.

Findings

Chaos observed in the system for certain parameters

Bifurcation diagrams illustrate regular and chaotic regimes

Lyapunov exponents and entropy quantify complexity

Abstract

Evolutionary motions in a bouncing ball system consisting of a ball having a free fall in the Earth's gravitational field have been studied systematically. Because of nonlinear form of the equations of motion, evolutions show chaos for certain set of parameters for certain initial conditions. Bifurcation diagram has been drawn to study regular and chaotic behavior. Numerical calculations have been performed to calculate Lyapunov exponents, topological entropies and correlation dimension as measures of complexity. Numerical results are shown through interesting graphics