Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative D^a±jbD^{\alpha\pm\jmath\beta}, 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.