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September 25, 2023


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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)

Course Curriculum

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

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