Introduction to Nonlinear Dynamics and Chaos: Deterministic Chaos, Fractals, History of Dynamics, Examples; Basic Concepts of Chaos Theory and Bifurcation Theory: Sensitive Dependence on Initial Conditions, The Butterfly Effect, Fixed points, Bifurcation, Stability, and the Feigenbaum constant; Fractals and Fractal dimension: The Similarity Dimension, Statistical Self-similarity, Koch curve, Sierpinski gasket and carpet, Example; One-Dimensional maps: Population growth and the Verhulst model, the logistic map, Graphical method; Lorenz Model and Strange Attractors: Chaos in the Weather, Lorenz Equations and Lorenz Attractor, Examples; Qualification of Chaos: Visual Inspection, Frequency Spectra, Lyapunov Exponents, Correlation Dimension; Attractor reconstruction: Time-delay Embedding, Takins’ embedding theorem, The Choice of Time-delay and Embedding Dimension, False Nearest Neighbor Algorithm, Autocorrelation Function, Estimation of Correlation Dimension and Largest Lyapunov exponent; Various Applications of the Course Material in Engineering Electronics, Robotics, Biological Sciences etc.

Suggested Text:

  1. Paul S. Addision, Fractals and Chaos: An illustrated course. IOP. 1997
  2. Strogatz, , Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Westview Press, 2001
  3. Photocopy material from various resources.