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Course

# 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
Home > Engineering > Electrical Engineering > Chaos, Fractals & Dynamical SystemsLectures:
• ### Lecture - 1 Representations of Dynamical Systems

00:54:56Prof. S. Banerjee
• ### Lecture - 2 Vector Fields of Nonlinear Systems

00:56:44Prof. S. Banerjee
• ### Lecture - 3 Limit Cycles

00:56:22Prof. S. Banerjee
• ### Lecture - 4 The Lorenz Equation - I

00:53:35Prof. S. Banerjee
• ### Lecture - 5 The Lorenz Equation - II

00:56:37Prof. S. Banerjee
• ### Lecture - 6 The Rossler Equation and Forced Pendulum

00:58:11Prof. S. Banerjee
• ### Lecture - 7 The Chua's Circuit

00:54:41Prof. S. Banerjee
• ### Lecture - 8 Discrete Time Dynamical Systems

00:55:37Prof. S. Banerjee
• ### Lecture - 9 The Logistic Map and Period doubling

00:55:25Prof. S. Banerjee
• ### Lecture - 10 Flip and Tangent Bifurcations

00:56:20Prof. S. Banerjee
• ### Lecture - 11 Intermittency Transcritical and pitchfork

00:55:31Prof. S. Banerjee
• ### Lecture - 12 Two Dimensional Maps

00:54:49Prof. S. Banerjee
• ### Lecture - 13 Bifurcations in Two Dimensional Maps

00:53:47Prof. S. Banerjee
• ### Lecture - 14 Introduction to Fractals

00:52:29Prof. S. Banerjee
• ### Lecture - 15 Mandelbrot Sets and Julia Sets

00:53:37Prof. S. Banerjee
• ### Lecture - 16 The Space Where Fractals Live

00:53:59Prof. S. Banerjee
• ### Lecture - 17 Interactive Function Systems

00:56:03Prof. S. Banerjee
• ### Lecture - 18 IFS Algorithms

00:55:00Prof. S. Banerjee
• ### Lecture - 19 Fractal Image Compression

00:51:25Prof. S. Banerjee
• ### Lecture - 20 Stable and Unstable Manifolds

00:55:24Prof. S. Banerjee
• ### Lecture - 21 Boundary Crisis and Interior Crisis

00:56:52Prof. S. Banerjee
• ### Lecture - 22 Statistics of Chaotic Attractors

00:57:04Prof. S. Banerjee
• ### Lecture - 23 Matrix Times Circle : Ellipse

00:52:26Prof. S. Banerjee
• ### Lecture - 24 Lyapunov Exponent

00:53:22Prof. S. Banerjee
• ### Lecture - 25 Frequency Spectra of Orbits

00:55:28Prof. S. Banerjee
• ### Lecture - 26 Dynamics on a Torus

00:54:41Prof. S. Banerjee
• ### Lecture - 27 Dynamics on a Torus

00:54:48Prof. S. Banerjee
• ### Lecture - 28 Analysis of Chaotic Time Series

00:56:10Prof. S. Banerjee
• ### Lecture - 29 Analysis of Chaotic Time Series

00:51:12Prof. S. Banerjee
• ### Lecture - 30 Lyapunou Function and Centre Manifold Theory

01:00:42Prof. S. Banerjee
• ### Lecture - 31 Non-Smooth Bifurcations

00:54:19Prof. S. Banerjee
• ### Lecture - 32 Non-Smooth Bifurcations

00:54:51Prof. S. Banerjee
• ### Lecture - 33 Normal from for Piecewise Smooth 2D Maps

00:54:10Prof. S. Banerjee
• ### Lecture - 34 Bifurcations in Piecewise Linear 2D Maps

00:55:32Prof. S. Banerjee
• ### Lecture - 35 Bifurcations in Piecewise Linear 2D Maps

00:52:59Prof. S. Banerjee
• ### Lecture - 36 Multiple Attractor Bifurcation and Dangerous

00:59:21Prof. S. Banerjee
• ### Lecture - 37 Dynamics of Discontinuous Maps

00:56:39Prof. S. Banerjee
• ### Lecture - 38 Introduction to Floquet Theory

00:57:11Prof. S. Banerjee
• ### Lecture - 39 The Monodromy Matrix and the Saltation Matrix

00:57:37Prof. S. Banerjee
• ### Lecture - 40 Control of Chaos

00:54:17Prof. S. Banerjee
Course Material: