Dynamical Systems with Applications using MATLAB by Stephen Lynch

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Dynamical Systems with Applications using MATLAB

PDF Free Download | Dynamical Systems with Applications using MATLAB 2nd Edition by Stephen Lynch

Contents of Dynamical Systems with Applications using MATLAB

  • A Tutorial Introduction to MATLAB
  • Tutorial One: The Basics and the Symbolic Math
  • Toolbox ( h)
  • Tutorial Two: Plots and Differential Equations ( h)
  • MATLAB Program Files or M-Files
  • Hints for Programming
  • MATLAB Exercises
  • References
  • Linear Discrete Dynamical Systems
  • Recurrence Relations
  • The Leslie Model
  • Harvesting and Culling Policies
  • MATLAB Commands
  • Nonlinear Discrete Dynamical Systems
  • The Tent Map and Graphical Iterations
  • Fixed Points and Periodic Orbits
  • The Logistic Map, Bifurcation Diagram,
  • and Feigenbaum Number
  • Gaussian and Hénon Maps
  • Applications
  • MATLAB Program Files
  • Complex Iterative Maps
  • Julia Sets and the Mandelbrot Set
  • Boundaries of Periodic Orbits
  • MATLAB Commands
  • Electromagnetic Waves and Optical Resonators
  • Maxwell’s Equations and Electromagnetic Waves
  • Historical Background
  • The Nonlinear SFR Resonator
  • Chaotic Attractors and Bistability
  • Linear Stability Analysis
  • Instabilities and Bistability
  • MATLAB Commands
  • Fractals and Multifractals
  • Construction of Simple Examples
  • Calculating Fractal Dimensions
  • A Multifractal Formalism
  • Multifractals in the Real World and Some Simple Examples
  • MATLAB Commands
  • The Image Processing Toolbox
  • Image Processing and Matrices
  • The Fast Fourier Transform
  • The Fast Fourier Transform on Images
  • Differential Equations
  • Simple Differential Equations and Applications
  • Applications to Chemical Kinetics
  • Applications to Electric Circuits
  • Existence and Uniqueness Theorem
  • MATLAB Commands
  • Planar Systems
  • Canonical Forms
  • Eigenvectors Defining Stable and Unstable Manifolds
  • Phase Portraits of Linear Systems in the Plane
  • Linearization and Hartman’s Theorem
  • Constructing Phase Plane Diagrams
  • MATLAB Commands
  • Interacting Species
  • Competing Species
  • Predator-Prey Models
  • Other Characteristics Affecting Interacting Species
  • MATLAB Commands
  • Limit Cycles
  • Historical Background
  • Existence and Uniqueness of Limit Cycles in the Plane
  • Nonexistence of Limit Cycles in the Plane
  • Perturbation Methods
  • MATLAB Commands
  • Hamiltonian Systems, Lyapunov Functions, and Stability
  • Hamiltonian Systems in the Plane
  • Lyapunov Functions and Stability
  • MATLAB Commands
  • Bifurcation Theory
  • Bifurcations of Nonlinear Systems in the Plane
  • Normal Forms
  • Multistability and Bistability
  • MATLAB Commands
  • Three-Dimensional Autonomous Systems and Chaos
  • Linear Systems and Canonical Forms
  • Nonlinear Systems and Stability
  • The Rossler System and Chaos
  • The Lorenz Equations, Chua’s Circuit, and the Belousov–Zhabotinski Reaction
  • MATLAB Commands
  • Poincare Maps and Nonautonomous Systems in the Plane
  • Poincare Maps
  • Hamiltonian Systems with Two Degrees of Freedom
  • Nonautonomous Systems in the Plane
  • MATLAB Commands
  • Local and Global Bifurcations
  • Small-Amplitude Limit Cycle Bifurcations
  • Melnikov Integrals and Bifurcating Limit Cycles
  • from a Center
  • Bifurcations Involving Homoclinic Loops
  • MATLAB and MuPAD Commands
  • The Second Part of Hilbert’s Sixteenth Problem
  • Statement of Problem and Main Results
  • Poincaré Compactification
  • Global Results for Liénard Systems
  • Local Results for Liénard Systems
  • Neural Networks
  • The Delta Learning Rule and Backpropagation
  • The Hopfield Network and Lyapunov Stability
  • Neurodynamics
  • MATLAB Commands
  • Chaos Control and Synchronization
  • Historical Background
  • Controlling Chaos in the Logistic Map
  • Controlling Chaos in the Hénon Map
  • Chaos Synchronization
  • MATLAB Commands
  • Binary Oscillator Computing
  • Brain-Inspired Computing
  • Oscillatory Threshold Logic
  • Applications and Future Work
  • MATLAB Commands
  • Simulink
  • Introduction
  • Electric Circuits
  • A Mechanical System
  • Nonlinear Optics
  • The Lorenz Equations and Chaos Synchronization

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