Forced van der Pol oscillator of complex order

Pinto, Carla; Tenreiro Machado, J. A.

http://hdl.handle.net/10400.22/13588

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Authors

Pinto, Carla

Tenreiro Machado, J. A.

Abstract(s)

In this paper it is considered a complex order forced van der Pol oscillator. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer derivative, where α = 1, β = 0. We compute amplitude and period values of the periodic solutions of the complex order forced van der Pol oscillator, for variation of distinct parameters such as forcing frequency, forcing amplitude and parameters α and β. We find interesting quasi-periodic motion for certain values of the forcing frequency. This type of behaviour is seen in the continuous forced van der Pol oscillator.