Introductory Non-Linear Dynamics

PRE-REQUISITES: Basic mathematics

COURSE OUTLINE: This course is designed to introduce students to the basic ideas of Dynamical systems, Stability, and chaos, largely using Iterative mappings as the model. The course will focus on qualitative ideas and will require students to explore dynamics through simulations (MATLAB will be adequate).

Chaos in Flows. The Lorenz and Rossler Systems..
Fractals.
Intermittency. Crises.
Lyapunov Exponents; Invariant measures.
Characterizing The Period-Doubling Route to Chaos.
Bifurcation Diagrams. Period 3 Implies Chaos. Characterizing Chaos.
Logistic map. Simple Examples of Bifurcations..
Maps & Flows. Simple Examples of Dynamics Systems-2.
Maps & Flows. Simple Examples of Dynamics Systems-1.
Introduction, Stability, Phase Space & Invariant Sets-3.
Introduction, Stability, Phase Space & Invariant Sets-2.
Introduction, Stability, Phase Space & Invariant Sets-1.
Intro.