Chaos Theory

This chapter presents an overview of chaos theory. It starts from the background of dynamical systems, presenting the mathematical representation and the concept of stability. Afterward, chaotic dynamics is explored from the horseshoe transformation, establishing that it is a consequence of the contraction-expansion-fold process. The main aspects of chaotic behavior are then discussed defining chaotic and fractal attractors. Routes to chaos are investigated showing some definitions of bifurcation, treating local and global bifurcations. Lyapunov exponents are defined in order to present a diagnostic tool for chaos.