title: Partially controlling transient chaos in the Lorenz equations.
abstract: Transient chaos is a characteristic behaviour in nonlinear dynamics where trajectories in a certain region of phase space behave chaotically for a while, before escaping to an external attractor. In some situations, the escapes are highly undesirable, so that it would be necessary to avoid such a situation. In this paper, we apply a control method known as partial control that allows one to prevent the escapes of the trajectories to the external attractors, keeping the trajectories in the chaotic region forever. We also show, for the first time, the application of this method in three dimensions, which is the major step forward in this work. To illustrate how the method works, we have chosen the Lorenz system for a choice of parameters where transient chaos appears, as a paradigmatic example in nonlinear dynamics. We analyse three quite different ways to implement the method. First, we apply this method by building an one-dimensional map using the successive maxima of one of the variables. Next, we implement it by building a two-dimensional map through a Poincaré section. Finally, we built a three-dimensional map, which has the advantage of using a fixed time interval between application of the control, which can be useful for practical applications.This article is part of the themed issue 'Horizons of cybernetical physics'.
authors.affiliation: Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
authors.forename: Rubén
authors.initials: R
authors.lastname: Capeáns
authors.affiliation: Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
authors.forename: Juan
authors.initials: J
authors.lastname: Sabuco
authors.affiliation: Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain miguel.sanjuan@urjc.es.
authors.forename: Miguel A F
authors.identifier: http://orcid.org/0000-0003-3515-0837
authors.initials: MA
authors.lastname: Sanjuán
authors.affiliation: Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA.
authors.forename: James A
authors.initials: JA
authors.lastname: Yorke
keywords: Lorenz system; chaos control; transient chaos