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Chaotic modelling and simulation : analysis of chaotic models, attractors and forms

Author: Christos H Skiadas; Charilaos Skiadas
Publisher: Boca Raton : CRC Press, ©2009.
Edition/Format:   eBook : Document : EnglishView all editions and formats

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Genre/Form: Electronic books
Additional Physical Format: Print version:
Skiadas, Christos H.
Chaotic modelling and simulation.
Boca Raton : CRC Press, ©2009
(DLC) 2008038183
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Christos H Skiadas; Charilaos Skiadas
ISBN: 9781420079012 1420079018
OCLC Number: 441946460
Notes: "A Chapman & Hall book."
Description: 1 online resource (349 pages) : illustrations
Contents: IntroductionChaos in Differential Equations Systems Chaos in Difference Equation SystemsMore Complex Structures Chaos and the Universe Odds and Ends and Milestones Models and Modeling Introduction Model Construction Modeling Techniques Chaotic Analysis and Simulation Deterministic, Stochastic, and Chaotic Models The Logistic Model The Logistic Map The Bifurcation Diagram Other Models with Similar BehaviorModels with Different Chaotic Behavior The GRM1 Chaotic ModelFurther DiscussionThe Delay Logistic Model Introduction Delay Difference ModelsTime Delay Differential EquationsA More Complicated Delay Model A Delay Differential Logistic Analogue Other Delay Logistic Models Model Behavior for Large Delays Another Delay Logistic ModelThe Henon Model Global Period Doubling Bifurcations in the Henon Map The Cosine-Henon Model An Example of Bifurcation and Period Doubling A Differential Equation Analogue Variants of the Henon Delay Difference Equation Variants of the Henon System EquationsThe Holmes and Sine Delay ModelsThree-Dimensional and Higher-Dimensional Models Equilibrium Points and Characteristic Matrices The Lotka-Volterra Model The Arneodo Model An Autocatalytic Attractor A Four-Dimensional Autocatalytic Attractor The Rossler ModelThe Lorenz ModelNonchaotic SystemsConservative SystemsLinear SystemsEgg-Shaped Forms Symmetric Forms More Complex Forms Higher-Order FormsRotations Introduction A Simple Rotation-Translation System of Differential Equations A Discrete Rotation-Translation Model A General Rotation-Translation Model Rotating Particles inside the Egg-Shaped Form Rotations Following an Inverse Square LawShape and Form Introduction Isometries in ModelingReflection and Translation Application in the Ikeda Attractor Chaotic Attractors and Rotation-Reflection Experimenting with Rotation and Reflection Chaotic Circular Forms Further AnalysisChaotic AdvectionThe Sink Problem Noncentral Sink Two Symmetric Sinks Chaotic Forms without Space ContractionOther Chaotic Forms Complex Sinusoidal Rotation Angle A Special Rotation-Translation Model Other Rotation-Translation ModelsChaos in Galaxies and Related Simulations Introduction Chaos in the Solar System Galaxy Models and Modeling Rotation-Reflection Relativity in Rotation-Translation Systems Other Relativistic Forms Galactic Clusters Relativistic Reflection-Translation Rotating Disks of Particles Rotating Particles under Distant Attracting Masses Two Equal Attracting Masses in Opposite Directions Galactic-Type Potentials and the Henon-Heiles SystemIntroduction The Henon-Heiles System Discrete Analogues to the Henon-Heiles System Paths of Particles in the Henon-Heiles System Other Forms for the HamiltonianThe Simplest Form for the HamiltonianGravitational Attraction A Logarithmic Potential Hamiltonians with a Galactic Type Potential: The Contopoulos SystemAnother Simple Hamiltonian SystemOdds and Ends Forced Nonlinear Oscillators The Effect of Noise in Three-Dimensional Models The Lotka-Volterra Theory for the Growth of Two Conflicting PopulationsThe PendulumA Special Second-Order Differential Equation Other Patterns and Chaotic FormsMilestones References List of Figures Index
Responsibility: Christos H. Skiadas, Charilaos Skiadas.


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