# Nonlinear Dynamical Systems

- Institution: IIT Bombay
- Department: Electrical Engineering
- Taught by: Prof. Harish K. Pillai, Prof. Madhu N.Belur
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108101002)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108101002)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [L1-Introduction](https://invisiblenetwork.ai/learn/nptel/108101002/5ca20abf0bb0) (Video)
2. [L2-First Order systems](https://invisiblenetwork.ai/learn/nptel/108101002/cdc9a044dd33) (Video)
3. [L3-Classification of Equilibrium points](https://invisiblenetwork.ai/learn/nptel/108101002/4a64166d0cfb) (Video)
4. [L4-Lipschitz Functions](https://invisiblenetwork.ai/learn/nptel/108101002/5a4e79d504db) (Video)
5. [L5-Existence/uniqueness theorems](https://invisiblenetwork.ai/learn/nptel/108101002/28dd17bfdb40) (Video)
6. [L6-Existence/uniqueness of solutions to differential equations](https://invisiblenetwork.ai/learn/nptel/108101002/0030cfa665a2) (Video)
7. [L7-Lyapunov theorem on stability](https://invisiblenetwork.ai/learn/nptel/108101002/4a82dae5dce0) (Video)
8. [L8-Extension of Lyapunov's Theorem in different contexts](https://invisiblenetwork.ai/learn/nptel/108101002/c5debf8d59a7) (Video)
9. [L9-LaSalle's Invariance principle, Barbashin and Krasovski theorems, periodic orbits](https://invisiblenetwork.ai/learn/nptel/108101002/5037893ee5c6) (Video)
10. [L10-Bendixson criterion and Poincare-Bendixson criterion. Example: Lotka Volterra predator prey model](https://invisiblenetwork.ai/learn/nptel/108101002/066ddc72e40b) (Video)
11. [L11-Bendixson and Poincare-Bendixson criteria van-der-Pol Oscillator](https://invisiblenetwork.ai/learn/nptel/108101002/0fd83b80f9c5) (Video)
12. [L12-Scilab simulation of Lotka Volterra predator prey model, van-der-Pol Oscillator Review of linearization, operating point/ operating trajectory](https://invisiblenetwork.ai/learn/nptel/108101002/c4900f78c231) (Video)
13. [L13-Signals, operators](https://invisiblenetwork.ai/learn/nptel/108101002/8fdc6091b16d) (Video)
14. [L14-Norms of signals, systems (operators), Finite gain L2 stable](https://invisiblenetwork.ai/learn/nptel/108101002/43fe54d34144) (Video)
15. [L15-Nyquist plots and Nyquist criterion for stability](https://invisiblenetwork.ai/learn/nptel/108101002/05e1f6f05f6b) (Video)
16. [L16-Interconnection between linear system & non-linearity, passive filters](https://invisiblenetwork.ai/learn/nptel/108101002/0065899cd37c) (Video)
17. [L17-Passive filters, Dissipation equality, positive real lemma](https://invisiblenetwork.ai/learn/nptel/108101002/2bc2661b7291) (Video)
18. [L18-Positive real lemma proof](https://invisiblenetwork.ai/learn/nptel/108101002/f61e909f163c) (Video)
19. [L19- Definition for positive realness and Kalman Yakubovich-Popov Theorem](https://invisiblenetwork.ai/learn/nptel/108101002/1f0e3c5da02c) (Video)
20. [L20-Kalman-Yakubovich-Popov Lemma/theorem and memoryless nonlinearities](https://invisiblenetwork.ai/learn/nptel/108101002/a87d8d45e604) (Video)
21. [L21-Loop tranformations and circle criterion](https://invisiblenetwork.ai/learn/nptel/108101002/716f578f4bf1) (Video)
22. [L22-Nonlinearities based on circle criterion](https://invisiblenetwork.ai/learn/nptel/108101002/a069a3b2c3cf) (Video)
23. [L23-Limit cycles](https://invisiblenetwork.ai/learn/nptel/108101002/895b67e1a3a0) (Video)
24. [L24-Popov criterion continuous, frequency-domain theorem](https://invisiblenetwork.ai/learn/nptel/108101002/029e3beff724) (Video)
25. [L25-Popov criterion continuous, frequency-domain theorem](https://invisiblenetwork.ai/learn/nptel/108101002/fafafffc30d2) (Video)
26. [L26-Describing function method](https://invisiblenetwork.ai/learn/nptel/108101002/93c8c1cb1298) (Video)
27. [L27-Describing Function :2](https://invisiblenetwork.ai/learn/nptel/108101002/05462127e2e6) (Video)
28. [L28-Describing : optimal gain](https://invisiblenetwork.ai/learn/nptel/108101002/e452739663fa) (Video)
29. [L29-Describing : optimal gain](https://invisiblenetwork.ai/learn/nptel/108101002/dc20ae72e848) (Video)
30. [L30-Describing function : Jump Hysteresis](https://invisiblenetwork.ai/learn/nptel/108101002/39d8e55a4871) (Video)
31. [L31-Describing functions : sufficient conditions for existence of periodic orbits non existence of periodic orbits](https://invisiblenetwork.ai/learn/nptel/108101002/694e3cc388d3) (Video)
32. [L32-Describing functions for nonlinearities](https://invisiblenetwork.ai/learn/nptel/108101002/1d0dc537a1a1) (Video)
33. [L33-Ideal relay with Hysteresis and dead zone](https://invisiblenetwork.ai/learn/nptel/108101002/e80761fcddfe) (Video)
34. [L34-Dynamical systems on manifolds-1](https://invisiblenetwork.ai/learn/nptel/108101002/5bb489261f3b) (Video)
35. [L35-Dynamical systems on manifolds-2](https://invisiblenetwork.ai/learn/nptel/108101002/0833087e17b1) (Video)