Investigating the Dynamics of the Kicked Double Rotor: a dynamical laboratory for discrete chaotic systems with 4D phase space

The study of nonlinear dynamical systems makes it possible to understand, apply and predict phenomena in several areas of scientific knowledge, ranging from meteorology and the dynamics of celestial bodies to population growth and brain synapses, anad many more. In view of its wide applicability, it is important to know basic tools used for analyzing dynamical systems. However, although many physical and engineering systems are described by multidimensional mathematical models, much of the introductory literature on the subject is limited to the study of systems with one or two-dimensional phase space. Therefore, this contribution aims to present, in a didactic way and employing a computational approach, basic tools to analyse systems with higher dimensional phase space, exploring how to obtain and interpret bifurcation diagrams, compute equilibrium points and analyse their stability and compute Lyapunov exponents. To do so, we will use a discrete time system with 4-dimensional phase space known as Pulsed Double Rotor as a dynamical laboratory.

Keywords
Chaotic maps; Stability analysis; Lyapunov exponents.