Course Details
Subject {L-T-P / C} : EE6343 : Nonlinear Dynamics and Chaos: Applications to Electrical Engineering { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Somnath Maity
Syllabus
Introduction: Phase space, deterministic versus stochastic modeling, finite vs infinite dimensional models, linear vs non-linear, autonomous vs non-autonomous systems. geometric approach to dynamical systems, fixed points, linearization, and stability
Dynamical systems: continuous vs discrete time, conservative vs dissipative Existence, uniqueness and smooth dependence of solutions of ODE's on initial conditions and parameters.
Bifurcations in one and two dimensional systems: Local vs global bifurcations, Implicit function theorem, classification of bifurcations, Some generalities: center manifold and normal form, symmetry and symmetry breaking, relation to catastrophes and sudden transitions.
Non-linear systems Analysis: Stable and unstable manifolds, conservative systems, reversible systems, Solution of (fully non-linear) damped pendulum equation, Limit cycles, relaxation oscillations, weakly non-linear oscillators, averaging method and two time-scales, Hopf bifurcation and oscillating power electrics systems, quasiperiodicity, coupled oscillators systems, nonlinear resonance and frequency locking.
Chaos and Fractal: Introduction, fixed points and cobwebs, Numerics and analysis of logistic map, periodic window, liapunov exponent, strange attractors and example. cantor sets, probabilistic constructions of fractals, fractals from deterministic systems, fractal basin boundaries, fractal dimension, correlation Dimension
Course Objectives
- To introduce and describe nonlinear phenomena in physical and engineering systems
- To understand fundamental characteristics of chaotic systems and how they are modelled
- To develop basic understanding of nonlinear phenomena using phase-plane diagrams, stable and unstable manifolds, and bifurcation analysis
- To learn about various applications of chaos in real-life systems and to control/ synchronize them
Course Outcomes
1. Acquire basic knowledge of nonlinear differential equations and iterative maps <br />2. Know about the properties of the most important strange attractors in discrete and continuous time <br />3. Improve communication skills by solving problems analytically, and training in solving nonlinear problems using numerical methods <br />4. Learn about various chaotic applications in real-life systems <br />5. Investigate the operational issues and limitations of practical converters in industrial applications.
Essential Reading
- S. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry And Engineering”, Perscus Book Publishing Group
- Kathleen T. Alligood,? Tim D. Sauer and,? James A. Yorke, Chaos: An Introduction to Dynamical Systems, Springer
Supplementary Reading
- H. B. Stewart, J. M. T. Thompson, Nonlinear Dynamics and Chaos, Wiley and Sons, NY, USA
- Robert C. Hilborn, Chaos and Nonlinear Dynamics, Oxford University Press