The Resource Chaos in Nature, (electronic resource)

Chaos in Nature, (electronic resource)

Label
Chaos in Nature
Title
Chaos in Nature
Creator
Contributor
Provider
Subject
Genre
Language
eng
Summary
Chaos theory deals with the description of motion (in a general sense) which cannot be predicted in the long term although produced by deterministic system, as well exemplified by meteorological phenomena. It directly comes from the Lunar theory - a three-body problem - and the difficulty encountered by astronomers to accurately predict the long-term evolution of the Moon using "Newtonian" mechanics. Henri Poincaré's deep intuitions were at the origin of chaos theory. They also led the meteorologist Edward Lorenz to draw the first chaotic attractor ever published. But the main idea consists of
Member of
Cataloging source
MHW
http://library.link/vocab/creatorName
Letellier, Christophe
Illustrations
illustrations
Index
index present
LC call number
Q172.5 .C45
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
ebrary
Series statement
World Scientific series on nonlinear science. Series A
Series volume
vol. 81
http://library.link/vocab/subjectName
  • Adaptive control
  • Chaotic behavior in systems
  • Mechanics, Analytic
  • Nonlinear theories
  • Chaotic behavior in systems
  • Mechanics, Analytic
  • Nonlinear theories
  • Celestial mechanics
  • SCIENCE
  • Celestial mechanics
  • Chaotic behavior in systems
  • Mechanics, Analytic
  • Nonlinear theories
Target audience
specialized
Label
Chaos in Nature, (electronic resource)
Instantiates
Publication
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Machine generated contents note: From Celestial Mechanics to Chaos -- 1.The Laws of Dynamics -- 1.1.Kepler's Empirical Laws -- 1.2.The Law of Gravitation -- 1.3.Theory of the Moon -- 2.The Three Body Problem -- 2.1.Imperfections in Newton's Theory -- 2.2.Challenges to the Law of Gravitation -- 2.3.Problem of the Convergence of Series -- 3.Simplification of the Three Body Problem -- 3.1.Simplification of the Geometry -- 3.2.Simplification of the General Equations -- 3.3.The First Exact Solutions -- 4.The Success of Celestial Mechanics -- 4.1.Perturbation Theory -- 4.2.The Theory of Jupiter and Saturn -- 4.3.The Theory of the Moon -- 4.4.Laplacian Determinism -- 4.5.The Discovery of Neptune -- 4.6.The Development of Perturbation Theory -- 5.Birth of the Global Approach -- 5.1.The Restricted Three-Body Problem -- 5.2.A Qualitative Approach -- 5.3.Studies of Sets of Solutions -- 5.4.Dynamical Systems -- 5.5.The Ideal Pendulum -- 5.6.The Poincare-Bendixon Theorem -- 5.7.Doubly Asymptotic Orbits -- 5.8.Deterministic but Unpredictable -- 6.The Stability of the Solar System -- 6.1.The Problem of Small Devisors -- 6.2.The KAM Theorem -- 6.3.A Model for the KAM Theorem -- 6.4.Numerical Approach -- Chaos in Nature: Properties and Examples -- 1.Periodic and Chaotic Oscillators -- 1.1.Oscillators and Degrees of Freedom -- 1.2.Damped Pendulum -- 1.3.Linear System of Two Oscillators -- 1.4.Nonlinear System of Two Oscillators -- 2.From Mathematics to Electronic Circuits -- 2.1.The Early Self-Oscillating Systems -- 2.1.1.The series dynamo machine -- 2.1.2.The musical arc -- 2.1.3.From vacuum tubes to oscillating valves -- 2.1.4.From the audion to the multivibrator -- 2.2.The First Dynamical Studies of Oscillators -- 2.2.1.Poincare's equation for the musical arc -- 2.2.2.Janet's equation for series dynamo machine -- 2.2.3.Blondel's equation for the triode -- 2.2.4.The van der Pol Equation -- 2.2.5.Some equations for the multivibrator and beyond -- 2.3.Relaxation Oscillations -- 2.3.1.First insights from the German school -- 2.3.2.Van der Pol's contribution -- 2.3.3.Relaxation oscillations in the real world -- 2.4.The First Computer Calculations -- 2.5.First Chaotic Attractors in Electronic Circuits -- 2.6.A Chaotic Thermionic Diode -- 3.From Meteorology to Chaos: The Second Wave -- 3.1.Prediction in Meteorology -- 3.2.The Lorenz System -- 3.2.1.Phase space -- 3.2.2.The stability of periodic solutions -- 3.2.3.Numerical integration and application of linear theory -- 3.2.4.Topological analysis -- 3.2.5.First-return map to maxima -- 3.3.Sensitivity to Initial Conditions -- 3.4.Turbulence, Aperiodic Solutions, and Chaos -- 3.5.Hydrodynamics and the Lorenz Attractor -- 3.6.Laser Dynamics and the Lorenz System -- 4.The Architecture of Chaotic Attractors -- 4.1.The Rossler System -- 4.1.1.A brief biography -- 4.1.2.Rossler's main influences -- 4.1.3.A chaotic chemical reaction -- 4.1.4.The Rossler system -- 4.1.5.A forgotten topological analysis -- 4.2.Poincare Section -- 4.3.Symbolic Dynamics -- 4.4.Topological Characterization -- 4.5.A Simple Model for the Poincare Map -- 4.6.Different Topologies for Chaos -- 5.Chemical Reactions -- 5.1.The Earliest Experiments -- 5.2.Chaos in an Experimental BZ-Reaction -- 5.3.Chaotic Copper Electrodissolution -- 6.Population Evolution -- 6.1.Theories of Malthus and Verhulst -- 6.2.A Model with Two Species -- 6.3.Models with Three Species -- 6.4.Observational Evidence -- 7.Chaos in Biology and Biomedicine -- 7.1.Glycolysis Oscillations -- 7.2.Fluctuations in Hematopoiesis -- 7.3.Cardiac Arrhythmias -- 7.3.1.The beginnings of electrophysiology -- 7.3.2.The heart --- An electric machine -- 7.3.3.Electrocardiograms and arrhythmias -- 7.3.4.Analysis of some heart rate variability -- 7.4.Patient Breathing with a Noninvasive Mechanical Ventilation -- 7.4.1.Early techniques for mechanical ventilation -- 7.4.2.Breathing variability under mechanical ventilation -- 7.5.Conclusion -- 8.Chaotically Variable Stars -- 8.1.The First Observations -- 8.2.The First Chaotic Models -- 8.3.Solar Activity -- 8.4.Chaotic Models of Solar Activity -- 9.Epilogue -- 9.1.The Fourth Dimension -- 9.2.A Weakly Dissipative System -- 9.3.Hyperchaotic Behavior -- 9.4.Toroidal Chaos -- 9.5.Simple Models and Complex Behavior
Dimensions
unknown
Extent
1 online resource (393 pages).
Form of item
online
Isbn
9789814374439
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Reproduction note
Electronic reproduction.
Specific material designation
remote
Stock number
421251
System control number
  • (OCoLC)826853971
  • (OCoLC)ocn826853971
Label
Chaos in Nature, (electronic resource)
Publication
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Machine generated contents note: From Celestial Mechanics to Chaos -- 1.The Laws of Dynamics -- 1.1.Kepler's Empirical Laws -- 1.2.The Law of Gravitation -- 1.3.Theory of the Moon -- 2.The Three Body Problem -- 2.1.Imperfections in Newton's Theory -- 2.2.Challenges to the Law of Gravitation -- 2.3.Problem of the Convergence of Series -- 3.Simplification of the Three Body Problem -- 3.1.Simplification of the Geometry -- 3.2.Simplification of the General Equations -- 3.3.The First Exact Solutions -- 4.The Success of Celestial Mechanics -- 4.1.Perturbation Theory -- 4.2.The Theory of Jupiter and Saturn -- 4.3.The Theory of the Moon -- 4.4.Laplacian Determinism -- 4.5.The Discovery of Neptune -- 4.6.The Development of Perturbation Theory -- 5.Birth of the Global Approach -- 5.1.The Restricted Three-Body Problem -- 5.2.A Qualitative Approach -- 5.3.Studies of Sets of Solutions -- 5.4.Dynamical Systems -- 5.5.The Ideal Pendulum -- 5.6.The Poincare-Bendixon Theorem -- 5.7.Doubly Asymptotic Orbits -- 5.8.Deterministic but Unpredictable -- 6.The Stability of the Solar System -- 6.1.The Problem of Small Devisors -- 6.2.The KAM Theorem -- 6.3.A Model for the KAM Theorem -- 6.4.Numerical Approach -- Chaos in Nature: Properties and Examples -- 1.Periodic and Chaotic Oscillators -- 1.1.Oscillators and Degrees of Freedom -- 1.2.Damped Pendulum -- 1.3.Linear System of Two Oscillators -- 1.4.Nonlinear System of Two Oscillators -- 2.From Mathematics to Electronic Circuits -- 2.1.The Early Self-Oscillating Systems -- 2.1.1.The series dynamo machine -- 2.1.2.The musical arc -- 2.1.3.From vacuum tubes to oscillating valves -- 2.1.4.From the audion to the multivibrator -- 2.2.The First Dynamical Studies of Oscillators -- 2.2.1.Poincare's equation for the musical arc -- 2.2.2.Janet's equation for series dynamo machine -- 2.2.3.Blondel's equation for the triode -- 2.2.4.The van der Pol Equation -- 2.2.5.Some equations for the multivibrator and beyond -- 2.3.Relaxation Oscillations -- 2.3.1.First insights from the German school -- 2.3.2.Van der Pol's contribution -- 2.3.3.Relaxation oscillations in the real world -- 2.4.The First Computer Calculations -- 2.5.First Chaotic Attractors in Electronic Circuits -- 2.6.A Chaotic Thermionic Diode -- 3.From Meteorology to Chaos: The Second Wave -- 3.1.Prediction in Meteorology -- 3.2.The Lorenz System -- 3.2.1.Phase space -- 3.2.2.The stability of periodic solutions -- 3.2.3.Numerical integration and application of linear theory -- 3.2.4.Topological analysis -- 3.2.5.First-return map to maxima -- 3.3.Sensitivity to Initial Conditions -- 3.4.Turbulence, Aperiodic Solutions, and Chaos -- 3.5.Hydrodynamics and the Lorenz Attractor -- 3.6.Laser Dynamics and the Lorenz System -- 4.The Architecture of Chaotic Attractors -- 4.1.The Rossler System -- 4.1.1.A brief biography -- 4.1.2.Rossler's main influences -- 4.1.3.A chaotic chemical reaction -- 4.1.4.The Rossler system -- 4.1.5.A forgotten topological analysis -- 4.2.Poincare Section -- 4.3.Symbolic Dynamics -- 4.4.Topological Characterization -- 4.5.A Simple Model for the Poincare Map -- 4.6.Different Topologies for Chaos -- 5.Chemical Reactions -- 5.1.The Earliest Experiments -- 5.2.Chaos in an Experimental BZ-Reaction -- 5.3.Chaotic Copper Electrodissolution -- 6.Population Evolution -- 6.1.Theories of Malthus and Verhulst -- 6.2.A Model with Two Species -- 6.3.Models with Three Species -- 6.4.Observational Evidence -- 7.Chaos in Biology and Biomedicine -- 7.1.Glycolysis Oscillations -- 7.2.Fluctuations in Hematopoiesis -- 7.3.Cardiac Arrhythmias -- 7.3.1.The beginnings of electrophysiology -- 7.3.2.The heart --- An electric machine -- 7.3.3.Electrocardiograms and arrhythmias -- 7.3.4.Analysis of some heart rate variability -- 7.4.Patient Breathing with a Noninvasive Mechanical Ventilation -- 7.4.1.Early techniques for mechanical ventilation -- 7.4.2.Breathing variability under mechanical ventilation -- 7.5.Conclusion -- 8.Chaotically Variable Stars -- 8.1.The First Observations -- 8.2.The First Chaotic Models -- 8.3.Solar Activity -- 8.4.Chaotic Models of Solar Activity -- 9.Epilogue -- 9.1.The Fourth Dimension -- 9.2.A Weakly Dissipative System -- 9.3.Hyperchaotic Behavior -- 9.4.Toroidal Chaos -- 9.5.Simple Models and Complex Behavior
Dimensions
unknown
Extent
1 online resource (393 pages).
Form of item
online
Isbn
9789814374439
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Reproduction note
Electronic reproduction.
Specific material designation
remote
Stock number
421251
System control number
  • (OCoLC)826853971
  • (OCoLC)ocn826853971

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