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Practical Numerical Algorithms for Chaotic Systems - Thomas S. Parker, Leon Chua
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Practical Numerical Algorithms for Chaotic Systems - new book

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Leon Chua; Thomas S. Parker:
Practical Numerical Algorithms for Chaotic Systems - new book

2012, ISBN: 9781461234869

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Leon Chua; Thomas S. Parker:
Practical Numerical Algorithms for Chaotic Systems - new book

2012, ISBN: 9781461234869

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Details of the book - Practical Numerical Algorithms for Chaotic Systems


EAN (ISBN-13): 9781461234869
Publishing year: 2012
Publisher: Springer New York

Book in our database since 2016-02-19T05:31:55-05:00 (New York)
Detail page last modified on 2023-01-15T08:15:06-05:00 (New York)
ISBN/EAN: 9781461234869

ISBN - alternate spelling:
978-1-4612-3486-9
Alternate spelling and related search-keywords:
Book author: leon chua, thomas parker
Book title: practical numerical, numerical algorithms


Information from Publisher

Author: Thomas S. Parker; Leon Chua
Title: Practical Numerical Algorithms for Chaotic Systems
Publisher: Springer; Springer US
348 Pages
Publishing year: 2012-12-06
New York; NY; US
Language: English
53,49 € (DE)
55,00 € (AT)
59,00 CHF (CH)
Available
XIV, 348 p.

EA; E107; eBook; Nonbooks, PBS / Mathematik/Sonstiges; Kybernetik und Systemtheorie; Verstehen; Nonlinear system; algorithms; bifurcation; stability; system; C; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Math. Applications in Chemistry; Computational Intelligence; Systems Theory, Control; Calculus of Variations and Optimization; Mathematical Applications in Chemistry; Computational Intelligence; Mathematics and Statistics; Optimierung; Quanten- und theoretische Chemie; Künstliche Intelligenz; BB

1 Steady-State Solutions.- 1.1 Systems.- 1.1.1 Autonomous continuous-time dynamical systems.- 1.1.2 Non-autonomous continuous-time dynamical systems.- 1.1.3 Relationship between autonomous and non-autonomous systems.- 1.1.4 Useful facts regarding continuous-time dynamical systems.- 1.1.5 Discrete-time systems.- 1.2 Limit sets.- 1.2.1 Equilibrium points.- 1.2.2 Periodic solutions.- 1.2.3 Quasi-periodic solutions.- 1.2.4 Chaos.- 1.2.5 Predictive power.- 1.3 Summary.- 2 Poincaré Maps.- 2.1 Definitions.- 2.1.1 The Poincaré map for non-autonomous systems.- 2.1.2 The Poincaré map for autonomous systems.- 2.2 Limit Sets.- 2.2.1 Equilibrium points.- 2.2.2 Periodic solutions.- 2.2.3 Quasi-periodic solutions.- 2.2.4 Chaos.- 2.3 Higher-order Poincaré maps.- 2.4 Algorithms.- 2.4.1 Choosing the hyperplane ?.- 2.4.2 Locating hyperplane crossings.- 2.5 Summary.- 3 Stability.- 3.1 Eigenvalues.- 3.2 Characteristic multipliers.- 3.2.1 Characteristic multipliers.- 3.2.2 Characteristic multipliers and the variational equation.- 3.2.3 Characteristic multipliers and equilibrium points.- 3.3 Lyapunov exponents.- 3.3.1 Definition.- 3.3.2 Lyapunov exponents of an equilibrium point.- 3.3.3 Lyapunov numbers of a fixed point.- 3.3.4 Perturbation subspaces.- 3.3.5 Lyapunov exponents of non-chaotic limit sets.- 3.3.6 Lyapunov exponents of chaotic attractors.- 3.4 Algorithms.- 3.4.1 Eigenvalues at an equilibrium point.- 3.4.2 Characteristic multipliers.- 3.4.3 Lyapunov exponents.- 3.5 Summary.- 4 Integration.- 4.1 Types.- 4.2 Integration error.- 4.2.1 Local errors.- 4.2.2 Global errors.- 4.2.3 Numerical stability.- 4.3 Stiff equations.- 4.4 Practical considerations.- 4.4.1 Variable step-size and order.- 4.4.2 Output points.- 4.4.3 Solving implicit equations.- 4.4.4 Error considerations.- 4.4.5 Integrating chaotic systems.- 4.4.6 Start-up costs.- 4.5 Summary.- 5 Locating Limit Sets.- 5.1 Introduction.- 5.1.1 Brute-force approach.- 5.1.2 Newton-Raphson approach.- 5.2 Equilibrium points.- 5.3 Fixed points.- 5.4 Closed orbits.- 5.5 Periodic solutions.- 5.5.1 The non-autonomous case.- 5.5.2 The autonomous case.- 5.6 Two-periodic solutions.- 5.6.1 Finite differences.- 5.6.2 Spectral balance.- 5.7 Chaotic solutions.- 5.8 Summary.- 6 Manifolds.- 6.1 Definitions and theory.- 6.1.1 Continuous-time systems.- 6.1.2 Discrete-time systems.- 6.2 Algorithms.- 6.2.1 Continuous-time systems.- 6.2.2 Discrete-time systems.- 6.3 Summary.- 7 Dimension.- 7.1 Dimension.- 7.1.1 Definitions.- 7.1.2 Algorithms.- 7.2 Reconstruction.- 7.3 Summary.- 8 Bifurcation Diagrams.- 8.1 Definitions.- 8.2 Algorithms.- 8.2.1 Brute force.- 8.2.2 Continuation.- 8.3 Summary.- 9 Programming.- 9.1 The user interface.- 9.1.1 The dynamical system interface.- 9.1.2 The program initialization interface.- 9.1.3 The interactive interface.- 9.2 Languages.- 9.2.1 Modular design.- 9.3 Library definitions.- 9.3.1 RKF—Runge-Kutta-Fehlberg integration.- 9.3.2 PARSE—input parsing routines.- 9.3.3 BINFILE—binary data files.- 9.3.4 GRAF—graphics.- 10 Phase Portraits.- 10.1 Trajectories.- 10.1.1 Selection of initial conditions.- 10.1.2 Calculating the trajectory.- 10.1.3 Arrowheads.- 10.1.4 Drawing the vector field.- 10.2 Limit sets.- 10.2.1 Equilibrium points.- 10.2.2 Limit cycles.- 10.2.3 Index.- 10.3 Basins.- 10.3.1 Definitions.- 10.3.2 Examples.- 10.3.3 Calculating boundaries of basins of attraction.- 10.4 Programming tips.- 10.4.1 Consistency checking.- 10.4.2 History files.- 10.5 Summary.- A The Newton-Raphson Algorithm.- B The Variational Equation.- C Differential Topology.- C.1 Differential topology.- C.2 Structural stability.- D The Poincaré Map.- E One Lyapunov Exponent Vanishes.- F Cantor Sets.- G List of Symbols.

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