EE651A, Nonlinear Systems, 2023-2024, Sem II

This is a course webpage for Nonlinear Systems offered in Sem II, 2023-2024.

Instructor

Abhilash Patel, apatel[at]iitk.ac.in

Teaching Assistants

Shikha Singh Chauhan (shikha22[at]iitk.ac.in), Sourabh Sen (sourabhsen22[at]iitk.ac.in)

Schedule

MWF, 9.00AM-10AM, at ACES 213

Announcements

11.02.2024: HW1 released through course email. Due 26.02.2024.
29.01.2024: Project/Term Paper Presentation II on 13.04.2024 (detailed instructions in course email)
29.01.2024: Project/Term Paper Presentation I on 02.03.2024 (detailed instructions in course email)
29.01.2024: Instructions regarding Class Project released through email.
27.01.2024: Office Hour
04.01.2024: Course webpage is live!

Lectures

Lecture	Topics	Suggested Readings (/ implies OR)
1	Course Mechanics	FCH
2	Introduction to Nonlinear Systems, Linear vs Nonlinear, Affine System	JW 1.1
3	Nonlinearity, Models, and Dynamical behaviours-I	JW 1.2//
4	Induced dynamical behaviours-II	JW 1.2/StS 6.2
5	Uniqueness and Existence, Tools from Matrix Theory	StS 2.5/6.2
6	Overview of NonLinear System Analysis,	JW Part I
7	Phase Plane, Homoclinic and Heteroclinc Orbit	JW 2.1-2.2/ StS 5.2
8	Hartman-Grobman Theorem, Linearization using Taylor Series	StS 6.3
9	Phase Portraits: Node, Saddle, Center, Focus, Extending to Nonlinear Systems, Heteroclinic and Homoclinic Orbits	JW 2.4-2.5/StS 5.2
10	Isoclines, Nullclines	StS 6.1.1/See Additional References

Additional References

An excellent class notes of Nonlinear Systems (Courtsey: Prof Murat Arcak) https://people.eecs.berkeley.edu/~arcak/resources/EE222ME237notesSp18.pdf
For additional reading on "Excitibility": http://www.math.utah.edu/~borisyuk/OLD_TEACHING/6770_Fall2017/excitability_types.pdf
For Nullclines related reading: https://npflueger.people.amherst.edu/math1b/Lecture33.pdf
For Floquet Theory: https://link.springer.com/article/10.1007/s12080-008-0016-2
For Lyapunov Approach for Limit Cycles: https://link.springer.com/content/pdf/10.1007/s11071-008-9398-3.pdf
For Incremental Stability & Convergent Dynamics: https://www.sciencedirect.com/science/article/pii/S0167691112002393
For Contraction Theory: https://www.sciencedirect.com/science/article/pii/S0005109898000193