In this article, we conclude our series of papers on the analysis and visualization of Chua attractors and their generalizations. We present a gallery of 144 n-scroll, 15 hyperchaotic and 37 synchronized systems. Along with time series and FFT we provide 3D visualizations; for some attractors we also supply Lyapunov coefficients and fractal dimensions. The goal in constructing our Gallery has been to make the general public aware of the enormous variety of chaotic phenomena and to change the widespread impression that they are isolated rarities. The Gallery provides a valuable collection of images and technical data which can be used to analyze these phenomena and to reproduce them in future studies. From a scientific point of view, we have tried to identify new methodological approaches to the study of chaos, opening nontraditional perspectives on the complexity of this domain. In our papers, we have discussed a broad range of topics, ranging from techniques for visualizing Chua attractors to computational methods allowing us to make a statistical classification of attractors' positions in phase space and to describe the evolutionary processes through which their shapes change over time. We see these processes as analogous to population dynamics in artificial environments. Within these environments, we use experimental methods to identify the models which guide morphogenetic change and which organize genetic landscapes in parameter space. This paper is organized as follows. First, we provide formal descriptions of the attractors generated by n-scroll, hyperchaotic and synchronized systems. The next section describes a Gallery of Chua attractors, generated by gradually varying the parameters and analyzing the resulting bifurcation maps. We then describe software tools allowing us to perform statistical analyses on selected sets of attractors, to visualize them, to explore their organization in phase space, and to conduct experimental investigations of the morphogenetic processes through which a small set of base attractors can generate a broad range of different forms. In the last section, we describe the creation of a Virtual 3D Gallery displaying some of the attractors we have presented in our six papers. The attractors are organized by theme, as they might be in a museum. The environment allows users to explore the attractors, interact with shapes, listen to music and sounds generated by the attractors, change their spatial organization, and create new shapes. To complete the paper-and the series-we propose a number of general conclusions.

A gallery of Chua attractors. Part VI

BILOTTA, Eleonora;PANTANO, Pietro Salvatore
2007

Abstract

In this article, we conclude our series of papers on the analysis and visualization of Chua attractors and their generalizations. We present a gallery of 144 n-scroll, 15 hyperchaotic and 37 synchronized systems. Along with time series and FFT we provide 3D visualizations; for some attractors we also supply Lyapunov coefficients and fractal dimensions. The goal in constructing our Gallery has been to make the general public aware of the enormous variety of chaotic phenomena and to change the widespread impression that they are isolated rarities. The Gallery provides a valuable collection of images and technical data which can be used to analyze these phenomena and to reproduce them in future studies. From a scientific point of view, we have tried to identify new methodological approaches to the study of chaos, opening nontraditional perspectives on the complexity of this domain. In our papers, we have discussed a broad range of topics, ranging from techniques for visualizing Chua attractors to computational methods allowing us to make a statistical classification of attractors' positions in phase space and to describe the evolutionary processes through which their shapes change over time. We see these processes as analogous to population dynamics in artificial environments. Within these environments, we use experimental methods to identify the models which guide morphogenetic change and which organize genetic landscapes in parameter space. This paper is organized as follows. First, we provide formal descriptions of the attractors generated by n-scroll, hyperchaotic and synchronized systems. The next section describes a Gallery of Chua attractors, generated by gradually varying the parameters and analyzing the resulting bifurcation maps. We then describe software tools allowing us to perform statistical analyses on selected sets of attractors, to visualize them, to explore their organization in phase space, and to conduct experimental investigations of the morphogenetic processes through which a small set of base attractors can generate a broad range of different forms. In the last section, we describe the creation of a Virtual 3D Gallery displaying some of the attractors we have presented in our six papers. The attractors are organized by theme, as they might be in a museum. The environment allows users to explore the attractors, interact with shapes, listen to music and sounds generated by the attractors, change their spatial organization, and create new shapes. To complete the paper-and the series-we propose a number of general conclusions.
Chua oscillator; n-scroll,; hyperchaotic and synchronized attractors
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/139738
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