File Name: chaos and nonlinear dynamics hilborn .zip
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Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Hilborn Published Computer Science. The phenomenology of chaos Towards a theory of nonlinear dynamics and chaos Quantifying chaos Special topics Appendices Index.
In this paper, we review modern nonlinear dynamical methods used in neuroscience and complex data analysis. We start with the general description of nonlinear dynamics, its geometrical and topological picture, as well as its extreme case, deterministic chaos, including its most popular models and methods: Lorenz attractor, Lyapunov exponents, and Kolmogorov—Sinai entropy. The main application of all presented tools is in various areas of medical diagnosis. Other applications include Grossberg—Arbib type brain modeling, autonomous robotics, nonlinear, and adaptive control, as well as nonlinear data classification. This is a preview of subscription content, access via your institution. Rent this article via DeepDyve.
This paper proposes a new three-dimensional chaotic flow with one stable equilibrium. Dynamical properties of this system are investigated. The system has a chaotic attractor coexisting with a stable equilibrium. Thus the chaotic attractor is hidden. Basin of attractions shows the tangle of different attractors. Also, some complexity measures of the system such as Lyapunov exponent and entropy will are analyzed.
Search this site. I know of no better introduction to the subject. Contains much valuable material Contains many computer examples and exercises that are useful and specific. It also has an extensive bibliography; which is a wonderfulresource Extremely useful. It provides lucid expositions of many important concepts as well as an extensive introduction to the literature of nonlinear dynamics.
This book introduces the full range of activity in the rapidly growing field of nonlinear dynamics. Using a step-by-step introduction to dynamics and geometry in state space as the central focus of understanding nonlinear dynamics, this book includes a thorough treatment of both differential equation models and iterated map models including a detailed derivation of the famous Feigenbaum numbers. It includes the increasingly important field of pattern formation and a survey of the controversial question of quantum chaos. Important tools such as Lyapunov exponents, fractal dimensions, and corr Important tools such as Lyapunov exponents, fractal dimensions, and correlation dimensions are treated in detail. Several appendices provide a detailed derivation of the Lorenz model from the Navier-Stokes equation, a summary of bifurcation theory, and some simple computer programs to study nonlinear dynamics. Each chapter includes an extensive, annotated bibliography.
Manuscript received November 7, ; final manuscript received March 6, ; published online June 14, Editor: Claude-Henri Lamarque. Habib, G. June 14, Nonlinear Dynam. January ; 8 1 : Precision and stability in position control of robots are critical parameters in many industrial applications where high accuracy is needed.
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Embed Size px x x x x Summary Further Reading Computer Exercises. Chaos is the term used to describe the apparently complex behavior of what we to be simple, well-behaved systems.
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