Amazon cover image
Image from Amazon.com

Deterministic and random evolution / Jens Lorenz, editor.

Contributor(s): Material type: TextTextSeries: Mathematics research developmentsPublisher: [Hauppauge], New York : Nova Science Publishers, Inc., [2013]Description: 1 online resourceContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781626180208
  • 1626180202
Subject(s): Genre/Form: Additional physical formats: Print version:: Deterministic and random evolutionDDC classification:
  • 519.3 23
LOC classification:
  • QA274.225
Online resources:
Contents:
DETERMINISTIC AND RANDOM EVOLUTION; DETERMINISTIC AND RANDOM EVOLUTION; Library of Congress Cataloging-in-Publication Data; Contents; Preface; Chapter 1: Introduction; Chapter 2: Basic Concepts; 1. Initial Value Problems for ODEs; 2. Discrete-Time Dynamics; 3. Continuous vs. Discrete Time; 4. Random Evolution; 5. Discussion; Chapter 3: Deterministic Systems: Outline of Advanced Topics; 1. Planetary Motion: Example for Determinism; 2. Reversibility in Time; 3. Sensitive Dependence on Initial Conditions; 4. Averages; 5. Dependence on Parameters; 6. Variation on Different Time Scales.
Chapter 4: Planetary Motion1. Outline; 2. The Two Body Problem: Reduction to One Body in a Central Field; 3. One Body in a Central Field; 4. The Equation for an Ellipse in Polar Coordinates; 5. The Kepler Orbit; 6. Kepler's Third Law; 7. Time Dependence; 8. Bessel Functions via a Generating Function: Integral Representation; 9. Discussion; Chapter 5: Is Time Reversible?; 1. Reversibility for the Two Body Problem; 2. Reversibility: General Definition; 3. Discussion; Chapter 6: The Bernoulli Shift and the Logistic Map; 1. The Bernoulli Shift: Definition.
2. The Bernoulli Shift: Dynamical Properties3. The Logistic Map and Its Relation to the Bernoulli Shift; 4. Average Behavior of the Logistic Map; Chapter 7: Evolution on Two Time-Scales; 1. Fast and Slow Time Scales; 2. Simple Example; 3. A Difficult Example; Chapter 8: Stability and Bifurcations; 1. Fixed Points; 2. Exponential Growth; 3. Logistic Growth; 4. The Delayed Logistic Map; 5. Parameter Dependent Evolution and Hysteresis; Chapter 9: Scripts; 1. Script for Logistic Growth; 2. Scripts for the Delayed Logistic Map; 3. Scripts for Parameter Dependent Evolution and Hysteresis.
Chapter 10: Two Oscillators: Periodicity, Ergodicity, and Phase Locking1. The Circle and the Two-Torus; 2. Uncoupled Oscillators: Periodic Solutions; 3. Uncoupled Oscillators: Ergodicity; 4. Time Average Equals Space Average for a Circle Map; 5. Coupled Oscillators; Chapter 11: The Gambler's Ruin Problem; 1. Description of the Game; 2. Some Questions and Numerical Realization; 3. The Transition Matrix P; 4. Evolution of Probability Density; 5. Discussion; 6. Application; 7. Script: Evolving the Probability Density for Gambler's Ruin; Chapter 12: Gambler's Ruin: Probabilities and Expected Time.
1. Probability of Ruin2. Probability of Winning; 3. Expected Time; 4. The Matrix View: Limit of Probability Densities; Chapter 13: Stochastic Model of a Simple Growth Process; 1. Growth Models; 2. The Forward Kolmogorov Equations; 3. Solution of the Forward Kolmogorov Equations; 4. The Sum of the pj(t); 5. The Expected Value of Xt; 6. The Variance of Xt; 7. Statistics of Interevent Times; 8. Numerical Realization of Random Evolution; 9. Figures and Scripts; Chapter 14: Introduction to Kinetic Theory; 1. Boyle, Bernoulli, Maxwell, and Sadi Carnot.
Item type:
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)
Holdings
Item type Home library Collection Call number Materials specified Status Date due Barcode
Electronic-Books Electronic-Books OPJGU Sonepat- Campus E-Books EBSCO Available

Includes bibliographical references (pages 183-184) and index.

Description based on print version record and CIP data provided by publisher.

DETERMINISTIC AND RANDOM EVOLUTION; DETERMINISTIC AND RANDOM EVOLUTION; Library of Congress Cataloging-in-Publication Data; Contents; Preface; Chapter 1: Introduction; Chapter 2: Basic Concepts; 1. Initial Value Problems for ODEs; 2. Discrete-Time Dynamics; 3. Continuous vs. Discrete Time; 4. Random Evolution; 5. Discussion; Chapter 3: Deterministic Systems: Outline of Advanced Topics; 1. Planetary Motion: Example for Determinism; 2. Reversibility in Time; 3. Sensitive Dependence on Initial Conditions; 4. Averages; 5. Dependence on Parameters; 6. Variation on Different Time Scales.

Chapter 4: Planetary Motion1. Outline; 2. The Two Body Problem: Reduction to One Body in a Central Field; 3. One Body in a Central Field; 4. The Equation for an Ellipse in Polar Coordinates; 5. The Kepler Orbit; 6. Kepler's Third Law; 7. Time Dependence; 8. Bessel Functions via a Generating Function: Integral Representation; 9. Discussion; Chapter 5: Is Time Reversible?; 1. Reversibility for the Two Body Problem; 2. Reversibility: General Definition; 3. Discussion; Chapter 6: The Bernoulli Shift and the Logistic Map; 1. The Bernoulli Shift: Definition.

2. The Bernoulli Shift: Dynamical Properties3. The Logistic Map and Its Relation to the Bernoulli Shift; 4. Average Behavior of the Logistic Map; Chapter 7: Evolution on Two Time-Scales; 1. Fast and Slow Time Scales; 2. Simple Example; 3. A Difficult Example; Chapter 8: Stability and Bifurcations; 1. Fixed Points; 2. Exponential Growth; 3. Logistic Growth; 4. The Delayed Logistic Map; 5. Parameter Dependent Evolution and Hysteresis; Chapter 9: Scripts; 1. Script for Logistic Growth; 2. Scripts for the Delayed Logistic Map; 3. Scripts for Parameter Dependent Evolution and Hysteresis.

Chapter 10: Two Oscillators: Periodicity, Ergodicity, and Phase Locking1. The Circle and the Two-Torus; 2. Uncoupled Oscillators: Periodic Solutions; 3. Uncoupled Oscillators: Ergodicity; 4. Time Average Equals Space Average for a Circle Map; 5. Coupled Oscillators; Chapter 11: The Gambler's Ruin Problem; 1. Description of the Game; 2. Some Questions and Numerical Realization; 3. The Transition Matrix P; 4. Evolution of Probability Density; 5. Discussion; 6. Application; 7. Script: Evolving the Probability Density for Gambler's Ruin; Chapter 12: Gambler's Ruin: Probabilities and Expected Time.

1. Probability of Ruin2. Probability of Winning; 3. Expected Time; 4. The Matrix View: Limit of Probability Densities; Chapter 13: Stochastic Model of a Simple Growth Process; 1. Growth Models; 2. The Forward Kolmogorov Equations; 3. Solution of the Forward Kolmogorov Equations; 4. The Sum of the pj(t); 5. The Expected Value of Xt; 6. The Variance of Xt; 7. Statistics of Interevent Times; 8. Numerical Realization of Random Evolution; 9. Figures and Scripts; Chapter 14: Introduction to Kinetic Theory; 1. Boyle, Bernoulli, Maxwell, and Sadi Carnot.

eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - Worldwide

There are no comments on this title.

to post a comment.

O.P. Jindal Global University, Sonepat-Narela Road, Sonepat, Haryana (India) - 131001

Send your feedback to glus@jgu.edu.in

Hosted, Implemented & Customized by: BestBookBuddies   |   Maintained by: Global Library