Introduction to Nonlinear Dynamics
Introduction to Nonlinear Dynamics . Instructor: Prof. Gaurav Raina, Department of Electrical Engineering, IIT Madras. This course is an introduction to nonlinear dynamics. We will employ a combination of analytical methods, examples, and geometric motivation. We will start with first order differential equations, and their bifurcations, and then move onto two dimensional flows.
(from nptel.ac.in )

A Brief Introduction to Modeling
VIDEO

Lecture 01 - A Brief Introduction to Modeling
Lecture 02 - Dynamics and Nonlinear Systems
Lecture 03 - 1-Dimensional Flows, Flows on the Line: Geometrical Intuition
Lecture 04 - 1-Dimensional Flows, Flows on the Line: Fixed Points and Stability
Lecture 05 - 1-Dimensional Flows, Flows on the Line: Local Stability Analysis
Lecture 06 - 1-Dimensional Flows, Flows on the Line: Existence and Uniqueness
Lecture 07 - 1-Dimensional Flows, Flows on the Line: Potentials
Lecture 08 - 1-Dimensional Flows, Flows on the Line: Numerical Methods
Lecture 09 - 1-Dimensional Flows, Bifurcations: Instruction
Lecture 10 - 1-Dimensional Flows, Bifurcations: Saddle Node
Lecture 11 - 1-Dimensional Flows, Bifurcations: Normal Forms
Lecture 12 - 1-Dimensional Flows, Bifurcations: Transcritical
Lecture 13 - 1-Dimensional Flows, Bifurcations: Pitchfork
Lecture 14 - 1-Dimensional Flows, Bifurcations: Imperfect
Lecture 15 - 1-Dimensional Flows, Flows on the Circle: Uniform Oscillator
Lecture 16 - 1-Dimensional Flows, Flows on the Circle: Nonuniform Oscillator
Lecture 17 - 2-Dimensional Flows, Linear Systems: Definitions and Examples
Lecture 18 - 2-Dimensional Flows, Linear Systems: Stability
Lecture 19 - 2-Dimensional Flows, Linear Systems: Classification
Lecture 20 - 2-Dimensional Flows, Linear Systems: Differential Equations
Lecture 21 - 2-Dimensional Flows, Phase Plane: Phase Portrait
Lecture 22 - 2-Dimensional Flows, Phase Plane: Existence, Uniqueness, Topological Consequences
Lecture 23 - 2-Dimensional Flows, Phase Plane: Fixed Points and Linearization
Lecture 24 - 2-Dimensional Flows, Limit Cycles: Introduction
Lecture 25 - 2-Dimensional Flows, Limit Cycles: Ruling Out Closed Orbits
Lecture 26 - 2-Dimensional Flows, Limit Cycles: Poincare Bendixson Theorem
Lecture 27 - 2-Dimensional Flows, Bifurcations: Saddle Node
Lecture 28 - 2-Dimensional Flows, Bifurcations: Transcritical and Pitchfork
Lecture 29 - 2-Dimensional Flows, Bifurcations: Hopf

References
Introduction to Nonlinear Dynamics
Instructor: Prof. Gaurav Raina, Department of Electrical Engineering, IIT Madras. This course is an introduction to nonlinear dynamics.