Carla Pinto, docente do Departamento de Matemática, apresenta a comunicação “Forced van der Pol Oscillator of Complex Order”, na 7ª Conferencia Europeia de Oscilações Não-lineares (7th European Nonlinear Oscillations Conference – ENOC 2011), agendada para 24-29 de Julho de 2011, na capital italiana.
ENOC 2011 Although the brand name ENOC (European Nonlinear Oscillations Conference) is still used as the historical abbreviation, the European Nonlinear Dynamics Conferences aim at covering the complete field of Nonlinear Dynamics, including Multibody Dynamics and coupling to Stability, Identification, Control and (Structural) Optimization. During the last few decades, the area of nonlinear dynamics has been evolving in a revolutionary way, with applications to a wide variety of engineering systems made possible by the use of sophisticated computational techniques employing powerful concepts and tools of dynamical systems, bifurcation and chaos theory.
FORCED VAN DER POL OSCILLATOR OF COMPLEX ORDER In this paper it is considered a complex order forced van der Pol oscillator. The complex derivative $D^{\alpha\pm\jmath\beta}$, with $\alpha,\beta\in\BBR^{+}$ is a generalization of the concept of integer derivative, where $\alpha=1,\ \beta=0.$. 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 $\alpha$ and $\beta$. 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.
A apresentação resulta de um artigo elaborado em colaboração com J. A. Tenreiro Machado, docente do Departamento de Engenharia Electrotécnica.
Palavras-chave: forced van der Pol oscillator, complex fractional order derivative, dynamical behavior, bifurcation
Instituto Superior de Engenharia do Porto