Chaos and Synchronization: An Unlikely Pair

We examine the defining characteristics of chaotic dynamical systems through thelens of three example systems. By analyzing the behavior of the logistic map, double pendulum, and Lorenz system we define chaos as aperiodic, deterministic behavior displayed by nonlinear dynamical systems that exhibit a sensitive dependence to initial conditions. We then develop some of the tools necessary to quantify chaotic behavior, including bifurcation diagrams, strange attractors in phase space, and Lyapunov exponents. Using the understanding of chaos developed prior, we proceed to study the synchronization of chaotic systems, including a subset of the available methods used to achieve synchronization. Additionally, we look at an example of coupled synchronization in communications applications