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
