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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
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