Venue: google-meet, see link below for the google-classroom
Class timings: TBA
First meeting: 23rd Feb 2021 10:00am
To join: https://bit D.O.T ly SLASH 3bg0P2l (hope you know what I mean!)
Course description:
Linear stability analysis, attractors, limit cycles, Poincare-Bendixson theorem, relaxation oscillations, elements of bifurcation theory: saddle-node, transcritical, pitchfork, Hopf bifurcations, integrability, Hamiltonian systems, Lotka-Volterra equations, Lyapunov function & direct method for stability, dissipative systems, Lorenz system, chaos & its measures, Lyapunov exponents, strange attractors, simple maps, period-doubling bifurcations, Feigenbaum constants, fractals. Both flows (continuous-time systems) & discrete-time systems (simple maps) will be discussed. Assignments will include numerical simulations.
Prerequisites, if any: familiarity with linear algebra - matrices, and ordinary differential equations
Desirable: Ability to write codes for solving simple problems.
Suggested books and references:
- S. Strogatz, Nonlinear Dynamics and Chaos: with Applications to physics, Biology, Chemistry, and Engineering, Westview, 1994.
- S. Wiggins, Introduction to applied nonlinear dynamics & chaos, Springer-Verlag, 2003.
- K. Alligood, T. Sauer, & James A.Yorke, Chaos: An Introduction to Dynamical Systems, Springer-Verlag, 1996.
- M.Tabor, Chaos and Integrability in Non-linear Dynamics, 1989.
- L. Ya. Adrianova, Introduction to Linear Systems of Differential Equations, AMS 1995.
- Morris W. Hirsch, Robert L. Devaney, Stephen Smale, Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press 2012.
Academic Events for this course:
|
|
Event |
From |
To |
|
1. |
First meeting |
23.02.2021 |
|
|
2. |
Course Registration |
22.02.2021 |
05.03.2021 |
|
3. |
Course Dropping without mention in the Transcripts |
06.03.2021 |
26.04.2021 |
|
3. |
Course Dropping with a mention in the Transcripts |
27.04.2021 |
26.05.2021 |
|
4. |
Last date for Instruction |
28.05.2021 |
|
|
5. |
Terminal Examination -- sometime between the dates of 02 to 11 June (exact date TBD) |
02.06.2021 |
11.06.2021 |
The course time will be adjusted in the first meeting based on any clashes that may arise, so those interested in registering should attend the first meeting without fail.
The mode of instruction will be completely online at least until 31st March. Further decisions will be announced in class.
Note:IISc semester schedule will be followed.
Interested ICTS students, please contact the instructor for
registration; Interested IISc students, please contact the IISc maths
department for registration process (note: IISc students need to
register for IISc course number MA 278).
google classroom link is https://classroom.google.com/u/0/c/Mjc1OTY1MTk3OTIw?cjc=jt67mhl
It is also mentioned on http://math.iisc.ac.in/course-schedule.html --
- Teacher: Amit Apte