ABSTRACT
This chapter presents a superficial overview on Dynamical System Theory (DST). DST is the branch of applied mathematics dedicated to qualitatively characterizing the long-term behavior of systems evolving according to difference and differential equations. The main goal of DST is to qualitatively determine the dynamics in the permanent regime of systems described by discrete and continuous-time nonlinear models. DST has its roots in classical mechanics, a major area in physics dealing with dynamics, kinematics, and statics of solids and fluids. Chaos is a limited and aperiodic behavior produced by a deterministic system exhibiting sensitive dependence on initial conditions. Chaos was predicted to occur in systems with a small number of variables by Poincare, in his work about the three-body problem. A simplistic overview of nonlinear dynamical systems and chaos is presented with a minimum of mathematical formalism.
