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Chaos, Fractals and Dynamic Systems

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)

Lecture 30 - Lyapunov Function and Centre Manifold Theory

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Lecture 01 - Representations of Dynamical Systems

Lecture 02 - Vector Fields of Nonlinear Systems

Lecture 03 - Limit Cycles

Lecture 04 - The Lorenz Equation I

Lecture 05 - The Lorenz Equation II

Lecture 06 - The Rossler Equation and Forced Pendulum

Lecture 07 - The Chua's Circuit

Lecture 08 - Discrete Time Dynamical Systems

Lecture 09 - The Logistic Map and Period Doubling

Lecture 10 - Flip and Tangent Bifurcations

Lecture 11 - Intermittency Transcritical and Pitchfork Bifurcations

Lecture 12 - Two Dimensional Maps

Lecture 13 - Bifurcations in Two Dimensional Maps

Lecture 14 - Introduction to Fractals

Lecture 15 - Mandelbrot Sets and Julia Sets

Lecture 16 - The Space where Fractals Live

Lecture 17 - Interactive Function Systems

Lecture 18 - IFS Algorithms

Lecture 19 - Fractal Image Compression

Lecture 20 - Stable and Unstable Manifolds

Lecture 21 - Boundary Crisis and Interior Crisis

Lecture 22 - Statistics of Chaotic Attractors

Lecture 23 - Matrix Times Circle: Ellipse

Lecture 24 - Lyapunov Exponent

Lecture 25 - Frequency Spectra of Orbits

Lecture 26 - Dynamics on a Torus

Lecture 27 - Dynamics on a Torus (cont.)

Lecture 28 - Analysis of Chaotic Time Series

Lecture 29 - Analysis of Chaotic Time Series (cont.)

Lecture 30 - Lyapunov Function and Centre Manifold Theory

Lecture 31 - Non-smooth Bifurcations

Lecture 32 - Non-smooth Bifurcations (cont.)

Lecture 33 - Normal Form for Piecewise Smooth 2D Maps

Lecture 34 - Bifurcations in Piecewise Linear 2D Maps

Lecture 35 - Bifurcations in Piecewise Linear 2D Maps (cont.)

Lecture 36 - Multiple Attractor Bifurcation and Dangerous Bifurcation

Lecture 37 - Dynamics of Discontinuous Maps

Lecture 38 - Introduction to Floquet Theory

Lecture 39 - The Monodromy Matrix and the Saltation Matrix

Lecture 40 - Control of Chaos