# Chaos, Fractals & Dynamical Systems

Indian Institute of Technology Kharagpur

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:

1. Representations of Dynamical Systems
2. Vector Fields of Nonlinear Systems
3. Limit Cycles
4. The Lorenz Equation - I
5. The Lorenz Equation - II
6. The Rossler Equation and Forced Pendulum
7. The Chua's Circuit
8. Discrete Time Dynamical Systems
9. The Logistic Map and Period doubling
10. Flip and Tangent Bifurcations
11. Intermittency Transcritical and pitchfork
12. Two Dimensional Maps
13. Bifurcations in Two Dimensional Maps
14. Introduction to Fractals
15. Mandelbrot Sets and Julia Sets
16. The Space Where Fractals Live
17. Interactive Function Systems
18. IFS Algorithms
19. Fractal Image Compression
20. Stable and Unstable Manifolds
21. Boundary Crisis and Interior Crisis
22. Statistics of Chaotic Attractors
23. Matrix Times Circle : Ellipse
24. Lyapunov Exponent
25. Frequency Spectra of Orbits
26. Dynamics on a Torus
27. Analysis of Chaotic Time Series
28. Lyapunou Function and Centre Manifold Theory
29. Non-Smooth Bifurcations
30. Normal from for Piecewise Smooth 2D Maps
31. Bifurcations in Piecewise Linear 2D Maps
32. Multiple Attractor Bifurcation and Dangerous
33. Dynamics of Discontinuous Maps
34. Introduction to Floquet Theory
35. The Monodromy Matrix and the Saltation Matrix
36. Control of Chaos
• ##### Lecture - 1 Representations of Dynamical Systems
Prof. S. Banerjee
• ##### Lecture - 2 Vector Fields of Nonlinear Systems
Prof. S. Banerjee
• ##### Lecture - 3 Limit Cycles
Prof. S. Banerjee
• ##### Lecture - 4 The Lorenz Equation - I
Prof. S. Banerjee
• ##### Lecture - 5 The Lorenz Equation - II
Prof. S. Banerjee
• ##### Lecture - 6 The Rossler Equation and Forced Pendulum
Prof. S. Banerjee
• ##### Lecture - 7 The Chua&#39;s Circuit
Prof. S. Banerjee
• ##### Lecture - 8 Discrete Time Dynamical Systems
Prof. S. Banerjee
• ##### Lecture - 9 The Logistic Map and Period doubling
Prof. S. Banerjee
• ##### Lecture - 10 Flip and Tangent Bifurcations
Prof. S. Banerjee
• ##### Lecture - 11 Intermittency Transcritical and pitchfork
Prof. S. Banerjee
• ##### Lecture - 12 Two Dimensional Maps
Prof. S. Banerjee
• ##### Lecture - 13 Bifurcations in Two Dimensional Maps
Prof. S. Banerjee
• ##### Lecture - 14 Introduction to Fractals
Prof. S. Banerjee
• ##### Lecture - 15 Mandelbrot Sets and Julia Sets
Prof. S. Banerjee
• ##### Lecture - 16 The Space Where Fractals Live
Prof. S. Banerjee
• ##### Lecture - 17 Interactive Function Systems
Prof. S. Banerjee
• ##### Lecture - 18 IFS Algorithms
Prof. S. Banerjee
• ##### Lecture - 19 Fractal Image Compression
Prof. S. Banerjee
• ##### Lecture - 20 Stable and Unstable Manifolds
Prof. S. Banerjee
• ##### Lecture - 21 Boundary Crisis and Interior Crisis
Prof. S. Banerjee
• ##### Lecture - 22 Statistics of Chaotic Attractors
Prof. S. Banerjee
• ##### Lecture - 23 Matrix Times Circle : Ellipse
Prof. S. Banerjee
• ##### Lecture - 24 Lyapunov Exponent
Prof. S. Banerjee
• ##### Lecture - 25 Frequency Spectra of Orbits
Prof. S. Banerjee
• ##### Lecture - 26 Dynamics on a Torus
Prof. S. Banerjee
• ##### Lecture - 27 Dynamics on a Torus
Prof. S. Banerjee
• ##### Lecture - 28 Analysis of Chaotic Time Series
Prof. S. Banerjee
• ##### Lecture - 29 Analysis of Chaotic Time Series
Prof. S. Banerjee
• ##### Lecture - 30 Lyapunou Function and Centre Manifold Theory
Prof. S. Banerjee
• ##### Lecture - 31 Non-Smooth Bifurcations
Prof. S. Banerjee
• ##### Lecture - 32 Non-Smooth Bifurcations
Prof. S. Banerjee
• ##### Lecture - 33 Normal from for Piecewise Smooth 2D Maps
Prof. S. Banerjee
• ##### Lecture - 34 Bifurcations in Piecewise Linear 2D Maps
Prof. S. Banerjee
• ##### Lecture - 35 Bifurcations in Piecewise Linear 2D Maps
Prof. S. Banerjee
• ##### Lecture - 36 Multiple Attractor Bifurcation and Dangerous
Prof. S. Banerjee
• ##### Lecture - 37 Dynamics of Discontinuous Maps
Prof. S. Banerjee
• ##### Lecture - 38 Introduction to Floquet Theory
Prof. S. Banerjee
• ##### Lecture - 39 The Monodromy Matrix and the Saltation Matrix
Prof. S. Banerjee
• ##### Lecture - 40 Control of Chaos
Prof. S. Banerjee