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Last updated:

September 25, 2023

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

Chaos, Fractals and Dynamic Systems. Instructor: Prof. S. Banerjee, Department of Electrical Engineering, IIT 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. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Representations of Dynamical Systems Unlimited
  • Lecture 02 – Vector Fields of Nonlinear Systems Unlimited
  • Lecture 03 – Limit Cycles Unlimited
  • Lecture 04 – The Lorenz Equation I Unlimited
  • Lecture 05 – The Lorenz Equation II Unlimited
  • Lecture 06 – The Rossler Equation and Forced Pendulum Unlimited
  • Lecture 07 – The Chua’s Circuit Unlimited
  • Lecture 08 – Discrete Time Dynamical Systems Unlimited
  • Lecture 09 – The Logistic Map and Period Doubling Unlimited
  • Lecture 10 – Flip and Tangent Bifurcations Unlimited
  • Lecture 11 – Intermittency Transcritical and Pitchfork Bifurcations Unlimited
  • Lecture 12 – Two Dimensional Maps Unlimited
  • Lecture 13 – Bifurcations in Two Dimensional Maps Unlimited
  • Lecture 14 – Introduction to Fractals Unlimited
  • Lecture 15 – Mandelbrot Sets and Julia Sets Unlimited
  • Lecture 16 – The Space where Fractals Live Unlimited
  • Lecture 17 – Interactive Function Systems Unlimited
  • Lecture 18 – IFS Algorithms Unlimited
  • Lecture 19 – Fractal Image Compression Unlimited
  • Lecture 20 – Stable and Unstable Manifolds Unlimited
  • Lecture 21 – Boundary Crisis and Interior Crisis Unlimited
  • Lecture 22 – Statistics of Chaotic Attractors Unlimited
  • Lecture 23 – Matrix Times Circle: Ellipse Unlimited
  • Lecture 24 – Lyapunov Exponent Unlimited
  • Lecture 25 – Frequency Spectra of Orbits Unlimited
  • Lecture 26 – Dynamics on a Torus Unlimited
  • Lecture 27 – Dynamics on a Torus (cont.) Unlimited
  • Lecture 28 – Analysis of Chaotic Time Series Unlimited
  • Lecture 29 – Analysis of Chaotic Time Series (cont.) Unlimited
  • Lecture 30 – Lyapunov Function and Centre Manifold Theory Unlimited
  • Lecture 31 – Non-smooth Bifurcations Unlimited
  • Lecture 32 – Non-smooth Bifurcations (cont.) Unlimited
  • Lecture 33 – Normal Form for Piecewise Smooth 2D Maps Unlimited
  • Lecture 34 – Bifurcations in Piecewise Linear 2D Maps Unlimited
  • Lecture 35 – Bifurcations in Piecewise Linear 2D Maps (cont.) Unlimited
  • Lecture 36 – Multiple Attractor Bifurcation and Dangerous Bifurcation Unlimited
  • Lecture 37 – Dynamics of Discontinuous Maps Unlimited
  • Lecture 38 – Introduction to Floquet Theory Unlimited
  • Lecture 39 – The Monodromy Matrix and the Saltation Matrix Unlimited
  • Lecture 40 – Control of Chaos Unlimited

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