Nonlinear dynamics : a hands-on introductory survey /

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 anal...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Roussel, Marc R., 1966- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan & Claypool Publishers, [2019]
Colección:IOP (Series). Release 6.
IOP concise physics.
Temas:
Dynamics.
Nonlinear theories.
Mathematical physics.
SCIENCE / Physics / Mathematical & Computational.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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