Chua Oscillator and its generalizations display a variety of chaotic behaviors, whose most startling manifestation is the presence of strange attractors. These come in many different shapes and sizes yet share a special kind of beauty. In the work reported in this paper, we explored the universe of these attractors - much of which is still virgin territory. We then recorded the most interesting and significant in a '' Gallery of Chua attractors ''. In papers, published in previous issues of this journal, we showed how different versions of the Oscillator follow different '' routes to chaos ''. Parts II-IV of the Gallery describe the attractors generated by the dimensional and dimensionless forms of the Oscillator as well as attractors generated by circuits with a cubic equation for the characteristic function of the Chua diode. Here, we provide a detailed discussion of single scroll Chua systems and present 248 attractors generated by such systems. For each attractor, we provide a three-dimensional image, time series and FFTs. We go on to describe the techniques used to create the Gallery and the main characteristics of the attractors it includes. We use techniques such as PCA to represent the gallery in parameter space. The same techniques allow us to manipulate the shape of the attractors by enlarging them along their main axes of development. We use Hausdor distances to compare shapes, and exploit the results to create landscapes in parameter space. Finally, we present experimental data from a single scroll attractor, using inertial ellipsoids and Hausdor. distances to show how the shape of the attractor evolves.

A gallery of Chua attractors. Part V

BILOTTA, Eleonora;PANTANO, Pietro Salvatore
2007

Abstract

Chua Oscillator and its generalizations display a variety of chaotic behaviors, whose most startling manifestation is the presence of strange attractors. These come in many different shapes and sizes yet share a special kind of beauty. In the work reported in this paper, we explored the universe of these attractors - much of which is still virgin territory. We then recorded the most interesting and significant in a '' Gallery of Chua attractors ''. In papers, published in previous issues of this journal, we showed how different versions of the Oscillator follow different '' routes to chaos ''. Parts II-IV of the Gallery describe the attractors generated by the dimensional and dimensionless forms of the Oscillator as well as attractors generated by circuits with a cubic equation for the characteristic function of the Chua diode. Here, we provide a detailed discussion of single scroll Chua systems and present 248 attractors generated by such systems. For each attractor, we provide a three-dimensional image, time series and FFTs. We go on to describe the techniques used to create the Gallery and the main characteristics of the attractors it includes. We use techniques such as PCA to represent the gallery in parameter space. The same techniques allow us to manipulate the shape of the attractors by enlarging them along their main axes of development. We use Hausdor distances to compare shapes, and exploit the results to create landscapes in parameter space. Finally, we present experimental data from a single scroll attractor, using inertial ellipsoids and Hausdor. distances to show how the shape of the attractor evolves.
Single scroll Chua systems; PCA and Hausdorff distances; patterns of morphogenesis
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/158632
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