Introduction to Nonlinear Dynamics of Electronic Systems: Tutorial

The study of chaos has generated enormous interest in exploring the complexity of the behavior in nature and in technology. Many of the important features of chaotic dynamical systems can be seen using experimental and computational methods in simple nonlinear mechanical systems or electronic circuits. Starting with the study of a chaotic nonlinear mechanical system (driven damped pendulum) or a nonlinear electronic system (circuit Chua) we introduce the reader into the concepts of chaos order in Sharkovsky's sense, and topological invariants (topological entropy and topological frequencies). The Kirchhoff's circuit laws are a pair of laws that deal with the conservation of charge and energy in electric circuits, and the algebraic theory of graphs characterizes these linear systems in terms of cycles and cocycles (or cuts). Here we discuss methods (topological semiconjugacy to piecewise linear maps and Markov graphs) to find a similar situation for the nonlinear dynamics, to understanding chaotic dynamics. Thus to chaotic dynamics we associate a Markov graph, where the dynamical and topological invariants will be seen as graph theoretical quantities.