Chaos, Fractals and Dynamic Systems


Lecture 1 - Representations of Dynamical Systems


Lecture 2 - Vector Fields of Nonlinear Systems


Lecture 3 - Limit Cycles


Lecture 4 - The Lorenz Equation - I


Lecture 5 - The Lorenz Equation - II


Lecture 6 - The Rossler Equation and Forced Pendulum


Lecture 7 - The Chua's Circuit


Lecture 8 - Discrete Time Dynamical Systems


Lecture 9 - The Logistic Map and Period doubling


Lecture 10 - Flip and Tangent Bifurcations


Lecture 11 - Intermittency Transcritical and pitchfork


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


Lecture 28 - Analysis of Chaotic Time Series


Lecture 29 - Analysis of Chaotic Time Series


Lecture 30 - Lyapunou Function and Centre Manifold Theory


Lecture 31 - Non-Smooth Bifurcations


Lecture 32 - Non-Smooth Bifurcations


Lecture 33 - Normal from for Piecewise Smooth 2D Maps


Lecture 34 - Bifurcations in Piecewise Linear 2D Maps


Lecture 35 - Bifurcations in Piecewise Linear 2D Maps


Lecture 36 - Multiple Attractor Bifurcation and Dangerous


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