basic electrical engineering

Chaos, Fractals & Dynamic Systems

Course Description

In this Course, We will learn about representations of Dynamical Systems, Vector Fields of Nonlinear Systems, Limit Cycles, The Lorenz Equation, The Rossler Equation and Forced Pendulum, The Chuas Circuit, Discrete Time Dynamical Systems, The Logistic Map and Period doubling, Flip and Tangent Bifurcations, Two Dimensional Maps, Introduction to Fractals, Mandelbrot Sets and Julia Sets, Interactive Function Systems, Fractal Image Compression, Boundary Crisis and Interior Crisis, Statistics of Chaotic Attractors, Lyapunov Exponent, Frequency Spectra of Orbits, Dynamics on a Torus, Control of Chaos, Non-Smooth Bifurcations, Introduction to Floquet Theory.

Course Objective

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 .

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