This is a course webpage for Nonlinear Systems offered in Sem II, 2023-2024.
Abhilash Patel, apatel[at]iitk.ac.in
Shikha Singh Chauhan (shikha22[at]iitk.ac.in), Sourabh Sen (sourabhsen22[at]iitk.ac.in)
MWF, 9.00AM-10AM, at ACES 213
| Lecture | Topics | Suggested Readings (/ implies OR) |
|---|---|---|
| 1 | Course Mechanics | FCH |
| 2 | Introduction to Non-Linear Systems | JW 1 |
| 3 | Nonlinearity and induced dynamical behaviours | StS 2.5 |
| 4 | Uniqueness and Existence, Tools from Matrix Theory | StS 6.2 |
| 5 | Non-Linear System Analysis | JW 2 |
| 6 | Phase Plane Analysis | JW 2.1-2.6 |
| 7 | Hartman-Grobman Theorem | StS 5.2 | 8 | Phase Plane: Saddle, Center, Focus, Extending to Nonlinear Systems, Heteroclinic and Homoclinic Orbit | StS 5.2 | 9 | Isoclines, Nullclines | StS 6.1.1/See Additional References | 10 | Exampls of Nullclines | StS 6.1.1/See Additional References | 11 | Notions of stability & convergence | JW 3.1-3.2 | 12 | Stability of Equilibrium, Lyapunov stability | JW 3.1-3.4 | 13 | Lyapunov Direct and Indirect Method | JW3.3-3.4 | 14 | Problems on Lyapunov Stability | JW 4.13 | 15 | Problems on Lyapunov Stability Contd. | JW 4.13 | 16 | LaSalle's Invariance Theorem | JW 3.4.3 | 17 | Problems on LaSalle's Invariance Theorem | JW 3.9 | 18 | Lyapunov stability for non-autonomous systems | JW 4.2 | 19 | Barbalat's Lemma, Lyapunov-like Lemma | JW 4.2 | 20 | Boundedness, Uniform Boundedness, Uniform Ultimate Boundedness | 21 | Input to State Stability(ISS) | 22 | Example of ISS | 23 | Stability of Limit Cycle | JW2.6 | 24 | Bifurcations:Saddle Node, Transcritical, Pitchfork, Hopf | StS 8.1, 8.2 |