CHAPTER 1 Computational Techniques of Linear Differential Equation
1.1 Basic concepts
1.2 First order linear differential equation
1.2.1 Separable equation
1.2.2 Linear equation
1.2.3 Exact equations and integrating factors
1.2.4 Direction fields
1.3 Second order differential equation
1.3.1 Homogeneous linear equation
1.3.2 Nonhomogeneous linear equation
1.4 First order differential equations
1.4.1 Basic theories of the first order DEs
1.4.2 Homogeneous linear DEs with constant coefficients
1.4.3 Nonhomogeneous linear DEs with constant coefficients
1.5 Three special methods
1.5.1 Laplace transform method
1.5.2 Power series method
1.5.3 Fourier series method
1.6 Numerical solution of differential equations
CHAPTER 2 Qualitative Analysis of Planar Differential Equations
2.1 Flow and manifold
2.1.1 Flow
2.1.2 Maniflod
2.2 Planar linear systems
2.3 Linearization of nonlinear systems
2.3.1 Singularities analysis of nonlinear systems
2.3.2 Stability of singularities
2.4 Periodic solutions of nonlinear systems
2.4.1 Orbit and limit set
2.4.2 Periodic orbit and limit cycle
2.5 Conservative system and dissipative system
2.5.1 Hamiltonian system
2.5.2 Dissipative systems
CHAPTER 3 Calculation and Analysis of Chaotic Systems
3.1 Attractor, Lyapunov exponent
3.1.1 Attractor
3.1.2 Lyapunov exponent
3.2 Center manifolds
3.2.1 Eigenspaces and manifolds
3.2.2 Center manifolds
3.3 Hopf bifurcation
3.3.1 Andmnov-Hopf bifurcation
3.3.2 Hopf bifurcation of Lorenz-like system
3.4 Dimension reduction analysis
3.4.1 Invariant algebraic surface
3.4.2 Invariant algebraic surface of T system
3.5 Infinity analysis
3.5.1 Poincare compactification on R2
3.5.2 Poincare compactification on R3
3.6 Melnikov method
CHAPTER 4 Control and Synchronization of Chaotic Systems
4.1 Feedback control
4.1.1 Feedback control of T system
4.1.2 Differential feedback control of Jerk system
4.2 Backstepping control
4.2.1 Backstepping for strict feedback systems
4.2.2 Adaptive backstepping control of electromechanical system
4.2.3 Adaptive backstepping control of T system
4.3 Periodic parametric perturbation control
4.3.1 Periodic parametric perturbation system
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