title: Clocking convergence to a stable limit cycle of a periodically driven nonlinear pendulum.
abstract: Convergence to a stable limit cycle of a periodically driven nonlinear pendulum is analyzed in this paper. The concept of the H-rank of a scalar sequence is used for the assessment of transient processes of the system. The circle map is used to illustrate the complex structure of the manifold of non-asymptotic convergence to a fixed point. It is demonstrated that the manifold of non-asymptotic convergence to a stable limit cycle also exists in the stroboscopic representation of the transient data of the periodically driven nonlinear pendulum. A simple method based on a short external impulse is proposed for the control of transient processes when the transition time to stable limit cycles must be minimized.
authors.affiliation: Research Group for Mathematical and Numerical Analysis of Dynamical Systems, Kaunas University of Technology, Studentu 50-222, Kaunas LT-51368, Lithuania. mantas.landauskas@ktu.lt
authors.forename: Mantas
authors.initials: M
authors.lastname: Landauskas
authors.forename: Minvydas
authors.initials: M
authors.lastname: Ragulskis