The course covers lessons in Representations of Dynamical Systems,Vector Fields of Nonlinear Systems, Limit Cycles, The Lorenz Equation, The Rossler Equation and Forced Pendulum, The Chua's Circuit, Discrete Time Dynamical Systems, The Logistic Map and Period doubling, Flip and Tangent Bifurcations, Intermittency Transcritical and pitchfork, Two Dimensional Maps, Mandelbrot Sets and Julia Sets, Stable and Unstable Manifolds ,The Monodromy Matrix and the Saltation Matrix.
Course topics:
- Representations of Dynamical Systems
- Vector Fields of Nonlinear Systems
- Limit Cycles
- The Lorenz Equation - I
- The Lorenz Equation - II
- The Rossler Equation and Forced Pendulum
- The Chua's Circuit
- Discrete Time Dynamical Systems
- The Logistic Map and Period doubling
- Flip and Tangent Bifurcations
- Intermittency Transcritical and pitchfork
- Two Dimensional Maps
- Bifurcations in Two Dimensional Maps
- Introduction to Fractals
- Mandelbrot Sets and Julia Sets
- The Space Where Fractals Live
- Interactive Function Systems
- IFS Algorithms
- Fractal Image Compression
- Stable and Unstable Manifolds
- Boundary Crisis and Interior Crisis
- Statistics of Chaotic Attractors
- Matrix Times Circle : Ellipse
- Lyapunov Exponent
- Frequency Spectra of Orbits
- Dynamics on a Torus
- Analysis of Chaotic Time Series
- Lyapunou Function and Centre Manifold Theory
- Non-Smooth Bifurcations
- Normal from for Piecewise Smooth 2D Maps
- Bifurcations in Piecewise Linear 2D Maps
- Multiple Attractor Bifurcation and Dangerous
- Dynamics of Discontinuous Maps
- Introduction to Floquet Theory
- The Monodromy Matrix and the Saltation Matrix
- Control of Chaos
