Nonlinear dynamics : a hands-on introductory survey / Marc R. Roussel.

Format:

Book

Author/Creator:

Roussel, Marc R., 1966- author.

Contributor:

Morgan & Claypool Publishers, publisher.

Institute of Physics (Great Britain), publisher.

Series:

IOP (Series). Release 6.

IOP concise physics

[IOP release 6]

IOP concise physics, 2053-2571

Language:

English

Subjects (All):

Dynamics.

Nonlinear theories.

Physical Description:

1 online resource (various pagings) : illustrations (some color).

Distribution:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019]

Place of Publication:

San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2019]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

text file

Biography/History:

Marc Roussel earned a Bachelor's degree in chemical physics from Queen's University in 1988. He then went on to graduate work in the Chemical Physics Theory Group at the University of Toronto under the supervision of Simon J. Fraser, earning an MSc in 1990 and a PhD in 1994. In 1995, Marc was hired as an Assistant Professor by the Department of Chemistry at the University of Lethbridge. He was promoted to Associate Professor in 2000, and to Professor in 2005.

Summary:

This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. This book also provides a survey that can be taught in a single academic term covering a greater variety of dynamical systems (discrete versus continuous time, finite versus infinite-dimensional, dissipative versus conservative) than is normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented.

Contents:

1. Introduction

1.1. What is a dynamical system?

1.2. The law of mass action

1.3. Software

2. Phase-plane analysis

2.1. Introduction

2.2. The Lindemann mechanism

2.3. Dimensionless equations

2.4. The vector field

2.5. Exercises

3. Stability analysis for ODEs

3.1. Linear stability analysis

3.2. Lyapunov functions

3.3. Exercises

4. Introduction to bifurcations

4.1. Introduction

4.2. Saddle-node bifurcation

4.3. Transcritical bifurcation

4.4. Andronov-Hopf bifurcations

4.5. Dynamics in three dimensions

4.6. Exercises

5. Bifurcation analysis with AUTO

5.1. Bifurcation diagram of a gene expression model

5.2. The phase diagram of Griffith's model

5.3. Bifurcation diagram of the autocatalator

5.4. Getting out of trouble in AUTO

5.5. Exercises

6. Invariant manifolds

6.1. Introduction

6.2. Flow dynamics away from the equilibrium point

6.3. Special eigenspaces of equilibrium points

6.4. From eigenspaces to invariant manifolds

6.5. Applications of invariant manifolds

6.6. Exercises

7. Singular perturbation theory

7.1. Introduction

7.2. Scaling and balancing

7.3. The outer solution

7.4. The inner solution

7.5. Matching the inner and outer solutions

7.6. Geometric singular perturbation theory and the outer solution

7.7. Exercises

8. Hamiltonian systems

8.1. Introduction

8.2. Integrable systems

8.3. Numerical integration

8.4. Exercises

9. Nonautonomous systems

9.1. Introduction

9.2. A driven Brusselator

9.3. Automated bifurcation analysis

9.4. Exercises

10. Maps and differential equations

10.1. Numerical methods as maps

10.2. Solution maps of differential equations

10.3. Poincaré maps of systems with periodic nonautonomous terms

10.4. Poincaré sections and maps in autonomous systems

10.5. Next-amplitude maps

10.6. Concluding comments

10.7. Exercises

11. Maps : stability and bifurcation analysis

11.1. Linear stability analysis of fixed points

11.2. Stability of periodic orbits

11.3. Lyapunov exponents

11.4. Exercises

12. Delay-differential equations

12.1. Introduction to infinite-dimensional dynamical systems

12.2. Introduction to delay-differential equations

12.3. Linearized stability analysis

12.4. Exercises

13. Reaction-diffusion equations

13.1. Introduction

13.2. Stability analysis of reaction-diffusion equations

13.3. Exercises

Appendix A. Software installation.

Notes:

"Version: 20190401"--Title page verso.

"A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.

Includes bibliographical references.

Title from PDF title page (viewed on May 6, 2019).

Other Format:

Print version:

ISBN:

9781643274645

9781643274621

OCLC:

1100643355

Access Restriction:

Restricted for use by site license.