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Complex order van der Pol oscillator

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Abstract

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

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Authors and Affiliations

  1. Centro de Matemática da Universidade do Porto and Department of Mathematics, Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    Carla M. A. Pinto

  2. Department of Electrical Engineering, Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072, Porto, Portugal

    J. A. Tenreiro Machado

Authors
  1. Carla M. A. Pinto
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  2. J. A. Tenreiro Machado
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Correspondence to Carla M. A. Pinto.

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Pinto, C.M.A., Tenreiro Machado, J.A. Complex order van der Pol oscillator. Nonlinear Dyn 65, 247–254 (2011). https://doi.org/10.1007/s11071-010-9886-0

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