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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)

Lecture 07 - 1-Dimensional Flows, Flows on the Line: Potentials

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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