Complex order van der Pol oscillator

• Author(s): Pinto, Carla M. A. ; Machado, J. A. Tenreiro
• Date: 2011
• Persistent ID: http://hdl.handle.net/10400.22/4141
• Origin: Repositório Científico do Instituto Politécnico do Porto
• Subject(s): Van der Pol oscillator; Complex order derivative; Dynamical behavior
• Document Type: Article
• Language: English

Description

In 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.