ABSTRACT
The analysis of complex dynamical behaviors begins with the study of a paradigmatic system that is able to reveal a broad variety of nonlinear phenomena despite its particularly simple structure, i.e., the logistic map. The analysis of the logistic map is performed by means of numerical and analytical calculations introducing the reader to the concept of bifurcation. Logistic map is a discrete-time dynamical system with only one state variable, a single parameter, and an elementary quadratic nonlinearity. For these reasons, the logistic map represents a structurally very simple dynamical system. The most important is the spectrum of Lyapunov exponents. The chapter introduces it referring to the logistic map, which is one-dimensional and discrete-time, but Lyapunov exponents can be defined and computed in the general case of multivariable and continuous-time systems. The Lyapunov exponents are a measure quantifying the high sensitivity of chaotic systems to initial conditions.
