NDLI: Rendering phase portraits and bifurcation diagrams in multidimensional oscillating systems

Content Provider	IEEE Xplore Digital Library
Author	Delrieux, C. Padin, M. Ramoscelli, G.
Copyright Year	2001
Description	Author affiliation: Univ. Nacional del Sur, Argentina (Delrieux, C.)
Abstract	Numerical simulation and visualization of nonlinear dynamical systems behavior can be easily produced, but these graphical results are of little aid if there are parameters in the system, perhaps causing it to exhibit some kind of qualitative change in its phase portrait bifurcations, or oscillations, for instance. For this reason, in this work we propose some methods to graphically detect, track and represent bifurcations and oscillatory behavior in the phase portrait. We propose an algorithm to advect the stationary behavior of the dynamic system and the representation of several periodic orbits in a higher dimension space. We consider two examples: a tunnel diode oscillator and the Colpitts oscillator. In both cases, our algorithm detects the different limit cycles that occur at different parameter values. These limit cycles are used to render the overall oscillatory behavior of the system as a 3D solid in parameter space.
Sponsorship	ATI (Informatics Professional Association,Spain)
Starting Page	58
Ending Page	67
File Size	1831569
Page Count	10
File Format	PDF
ISBN	0769513964
ISSN	15224902
DOI	10.1109/SCCC.2001.972632
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-11-09
Publisher Place	Chile
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Visualization Change detection algorithms Limit-cycles Bifurcation Rendering (computer graphics) Numerical simulation Orbits Nonlinear dynamical systems Oscillators Phase detection
Content Type	Text
Resource Type	Article

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