Eur. Phys. J. B (2018) 91: 144
https://doi.org/10.1140/epjb/e2018-90295-1

Regular Article

On symmetric and asymmetric Van der Pol-Duffing oscillators

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

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

Received: 27 April 2018
Received in final form: 8 May 2018
Published online: 2 July 2018

Abstract

We investigate numerically the dynamics of both symmetric and asymmetric Van der Pol-Duffing oscillators driven by a periodic force F(t) = f cosωt. Each system is modeled by a different second order nonautonomous nonlinear ordinary differential equation controlled by five parameters. Our investigation takes into account the (ω, f) parameter-space in the two systems, keeping the other three parameters fixed. We verify the existence of parameter regions for which the corresponding trajectories in the phase-space are periodic, quasiperiodic, and chaotic, for the symmetric case. In the asymmetric case we verify the existence only of periodic and chaotic regions in the (ω, f) parameter-space. Finally, we also investigate the organization of the dynamics in the two systems, identifying Fibonacci and period-adding sequences of periodic structures.