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Nonlinear dynamics : a hands-on introductory survey

Author: Marc R Roussel; Morgan & Claypool Publishers,; Institute of Physics (Great Britain),
Publisher: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2019] [2019]
Series: IOP concise physics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Marc R Roussel; Morgan & Claypool Publishers,; Institute of Physics (Great Britain),
ISBN: 9781643274645 1643274643 9781643274621 1643274627 1643274619 9781643274614
OCLC Number: 1100643355
Notes: "Version: 20190401"--Title page verso.
"A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.
Description: 1 online resource : illustrations (some color).
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.
Series Title: IOP concise physics.
Responsibility: Marc R. Roussel.

Abstract:

Uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab and the Maple symbolic algebra system. Detailed  Read more...

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