Chaos prediction and bifurcation analysis in control engineering

Abstract

In this paper, two different methods to compute the period-doubling route to chaos (or Feigenbaum chaos) in nonlinear systems are presented. The first one is a semi-analytical procedure, based on a symbolic calculation of an approximate monodromy matrix. The second one takes advantage of software packages for continuation of periodic solutions. Both procedures are used to analyze Chua´s circuit. The second method is also applied to the Rössler system and one of the chaotic systems of Sprott. In all three cases, several period-doubling bifurcation points in the parameter space are detected, allowing to compute a sequence of values supposedly converging to Feigenbaum´s constant. This "experimental´´ computer verification agrees with experiments performed by other researchers in real systems. This material has been used in final projects in a graduate course in dynamical systems.