Fractional damping induces resonant behavior in the Duffing oscillator
Mattia Coccolo, Jesús M. Seoane, Miguel A. F. Sanjuán
Abstract
The interaction between the fractional order parameter and the damping parameter can play a relevant role for introducing different dynamical behaviors in a physical system. Here, we study the Duffing oscillator with a fractional damping term. Our findings show that for certain values of the fractional order parameter, the damping parameter, and the forcing amplitude high oscillations amplitude can be induced. This phenomenon is due to the appearance of a resonance in the Duffing oscillator only when the damping term is fractional. • Fractional damping induces complex phenomena which do not exist in the non-fractional case. • Existence and characterization of the resonant phenomenon induced by the fractional order parameter. • Analysis of the complex dynamics induced by the fractional order parameter.