Utilize este identificador para referenciar este registo: http://hdl.handle.net/10400.22/4136
Título: Complex-order forced van der Pol oscillator
Autor: Pinto, Carla M.A.
Machado, J.A.Tenreiro
Palavras-chave: Complex-order derivative
Dynamical behavior
Forced van der Pol oscillator
Data: 2011
Editora: SAGE Publications
Relatório da Série N.º: Journal of Vibration and Control;
Resumo: In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.
Peer review: yes
URI: http://hdl.handle.net/10400.22/4136
ISSN: 1077-5463
Versão do Editor: http://jvc.sagepub.com/content/18/14/2201
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