# InfoCoBuild

## 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

 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.