Complex order van der Pol oscillator

Carla M. A. Pinto (1) , J. A. Tenreiro machado (2)

1 CMUP - Centro de Matemática - Universidade do Porto
2 Department of Electrical Engineering

In this paper a complex-order van der Pol oscillator is considered. The complex derivative , with ,∈ 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 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.

Mots clés: Van der Pol oscillator; Complex order derivative; Dynamical behavior

Carla M. A. Pinto, J. A. Tenreiro machado. Complex order van der Pol oscillator. Nonlinear Dynamics, 2010, 65 (3), pp.247-254. ⟨10.1007/s11071-010-9886-0⟩. ⟨hal-00640454⟩