Eur. Phys. J. B (2014) 87: 196
https://doi.org/10.1140/epjb/e2014-50368-9

Regular Article

Organization of periodic structures in a damped-forced oscillator

Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville, Brazil

^a e-mail: paulo.rech@udesc.br

Received: 6 June 2014
Received in final form: 30 June 2014
Published online: 9 September 2014

Abstract

We report on the dynamics in a parameter plane of a continuous-time damped system driven by a periodic forcing. The dynamics is characterized by considering the Lyapunov exponents spectrum and conventional bifurcation diagrams, to discriminate periodic, quasiperiodic, and chaotic behaviors for each point in this parameter plane, according two parameters are simultaneously varied. Periodic structures born in a quasiperiodic region and embedded in a chaotic region, the so-called Arnold tongues, are observed. We show that the Arnold tongues periodic distribution is highly organized in a mixed set of two period-adding sequences. Other three typical periodic structures born and embedded in a chaotic region were observed, also individually organized in a mixed set of two period-adding sequences.