On symmetric and asymmetric Van der Pol-Duffing oscillators

Vinícius Wiggers and Paulo C. Rech ()
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Vinícius Wiggers: Departamento de Física, Universidade do Estado de Santa Catarina
Paulo C. Rech: Departamento de Física, Universidade do Estado de Santa Catarina

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 7, 1-6

Abstract: 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.

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1140/epjb/e2018-90295-1

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