Optimal chaos control and discretization algorithms

Abstract: A new type of chaos control based on Optimal Discretization Algorithm (ODA) is described. The approach optimizes the complexity of a given dynamical system through variation of discretization parameters. In particular, a chaotic system can be transformed into a system with various numbers of discrete cycles. As the first step, applications of ODA are restricted to a special but instructive case of dynamical systems with a single chaotic attractor. The description of ODA is supplemented by a motivated introduction of its components with emphasis on those that are crucial for obtaining optimal and generalized results. The approach is illustrated in four examples of dynamical systems: Lorenz, Controlled Duffing, Rössler, and Controlled Pendulum. [Copyright &y& Elsevier]