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- Forced van der Pol oscillator of complex orderPublication . Pinto, Carla; Tenreiro Machado, J. A.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.
- Complex order van der Pol oscillatorPublication . Pinto, Carla M.A.; Machado, J.A.TenreiroIn this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.
- Complex order van der Pol oscillatorPublication . Pinto, Carla; Tenreiro Machado, J. A.In this paper it is considered a complex order van der Pol oscillator. A complex derivative D®§|¯, with ®; ¯ 2 R+ is a generalization of the concept of integer derivative, where ® = 1; ¯ = 0: By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the complex order van der Pol oscillator, are studied for variation of these parameters.