A gallery of Chua attractors / Eleonora Bilotta, Pietro Pantano.

Includes bibliographical references and index.

Ch. 1. Chua's oscillator and its generalizations. 1. Introduction. 2. Chua oscillator. 3. Diode with cubic function. 4. n-Scroll attractors. 5. From chaos to hyperchaos. 6. A gallery of Chua attractors. 7. Conclusions -- ch. 2. The physical circuit. 1. Introduction. 2. A gallery of attractors. 3. Visualization issues. 4. Conclusions -- ch. 3. Dimensionless equations. 1. Introduction. 2. Information seeking in chaos domain. 3. The main features of the gallery. 4. Representing parameter space. 5. Conclusions -- ch. 4. The cubic equation. 1. Introduction. 2. A gallery of attractors. 3. Representations of parameter space. 4. Laws of morphogenesis. 5. Shape distance in phase space. 6. Conclusions -- ch. 5. Single-scroll systems. 1. Introduction. 2. The gallery of attractors. 3. Representing attractors in parameter space. 4. Visualizing the parameter space: the inertial ellipsoid method. 5. Visualizing parameter space: The Hausdorff distance method. 6. Conclusions -- ch. 6. Multiscrolls systems. 1. Introduction. 2. Formal aspects of n-Scroll, hyper-chaotic and synchronized systems. 3. The Gallery. 4. Computational tools. 5. The virtual museum and the navigable galleries. 6. Conclusions.

Chaos is considered as one of the most important concepts in modern science. It originally appeared only in computer simulation (the famous Lorenz equation of 1963), but this changed with the introduction of Chua's oscillator (1986) - a simple electronic circuit with the ability to generate a vast range of chaotic behaviors. With Chua's circuit, chaos became a physical phenomenon, readily understood and represented in mathematical language. Yet, even so, it is still difficult for the non-specialist to appreciate the full variety of behaviors that the system can produce. This book aims to bridge the gap. A gallery of nearly 900 "chaotic attractors"--Some generated by Chua's physical circuit, the majority through computer simulation of the circuit and its generalizations - are illustrated as 3D color images, time series and fast Fourier transform algorithms. For interested researchers, also presented is the information necessary to replicate the behaviors and images. Finally, how the fractal richness can be plied to artistic ends in generating music and interesting sounds is shown; some examples are included in the DVD-ROM which comes with the book.

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