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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)

Representations of Dynamical Systems


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

References
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, ...