title: Dissipative dynamics of a particle in a vibrating periodic potential: Chaos and control.
abstract: The dissipative chaotic dynamics of a particle subjected to a horizontally vibrating periodic potential is characterized theoretically and confirmed numerically in the case of an external chaos-controlling periodic excitation also acting on the particle. Theoretical predictions concerning the chaotic threshold in parameter space are deduced from the application of Melnikov's method that fully determine the chaos-control scenario. Also, the structure of diverse regularization regions in parameter space is explained theoretically with the aid of an energy analysis. It was found that the phase difference between the two periodic excitations involved plays a crucial role in the chaos-control scenario, with the particular feature that its optimal value depends upon the ratio between the damping coefficient and the excitation frequency. This constitutes a genuine feature of the chaos-control scenario associated with nonsteady potentials which is in contrast to the case of steady potentials. Additionally, we demonstrate the robustness of the chaos-control scenario against the presence of low-intensity Gaussian noise and reshaping of chaos-suppressing excitations.
authors.affiliation: Departamento de Física Aplicada, E.I.I., Universidad de Extremadura, Apartado Postal 382, E-06006 Badajoz, Spain and Instituto de Computación Científica Avanzada, Universidad de Extremadura, E-06006 Badajoz, Spain.
authors.forename: R
authors.initials: R
authors.lastname: Chacón
authors.affiliation: Departamento de Física Aplicada, E.I.N.A., Universidad de Zaragoza, E-50018 Zaragoza, Spain and Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, E-50009 Zaragoza, Spain.
authors.forename: P J
authors.initials: PJ
authors.lastname: Martínez
authors.affiliation: Departamento de Ingeniería Eléctrica, Electrónica y Automática, Escuela de Ingenierías Industriales, Universidad de Castilla-La Mancha, E-02071 Albacete, Spain.
authors.forename: J A
authors.initials: JA
authors.lastname: Martínez