TEW - Ordinary Differential Equations, Dynamical Systems and Chaos using Matlab
Speakers and Syllabus
Speakers and Tutors
Name of the Speaker with affiliation | No. of Lectures | Detailed Syllabus |
Dr. Madhukant Sharma Assistant Professor, DA- IICT Gandhinagar |
7 hrs | Existence and uniqueness of solutions for first order ODEs, Systems of first order ODEs and higher order ordinary differential equations with applications; Laplace Transform and its Application to Differential Equations; Numerical Methods for ODEs (IVPs): Euler’s Method, Higher order Taylor’s Method, Runge-Kutta Method, Stability and Convergence. Basics in Matlab, the symbolic math toolbox, plots and differential equations. |
Prof. Syed Abbas, Professor, IIT Mandi | 6 hrs | Stability, stability of linear systems, continuous dependence and stability properties, linear systems, two dimensional systems, stability by Lyapunov method, autonomous and non-autonomous systems. |
Dr. Mukesh Tiwari, Associate Professor, DA- IICT Gandhinagar | 11 hrs | Discrete Dynamical Systems: Iterative maps: Logistic map, tent map, Fixed points and periodic orbits, Stability analysis: Linearization, Jacobian matrix, Cobweb Method: Graphical analysis of iterations. Continuous Dynamical Systems: Phase portraits and vector fields, Fixed points and stability in continuous systems: Linear stability analysis. Nonlinear Dynamics and Chaos: Bifurcations: Saddle-node, transcritical, pitchfork, Hopf bifurcations, Examples and real-world applications of bifurcations. Introduction to Chaos, Lorenz attractor, Sensitivity to initial conditions: Butterfly effect, Lyapunov exponents and their significance, Strange attractors and fractals, Visualizing chaotic attractors. Chaos in Discrete Systems: Detailed study of the logistic map, Period-doubling route to chaos, Bifurcation diagram and its interpretation, Numerical methods for exploring chaos. |
References:
- Shair Ahmad, M. Rama Mohana Rao, Theory of ordinary differential equations: with applications of biology and engineering, Affiliated East-West Private Lmt., New Delhi [India], ©1999
- Morris W. Hirsch, Stephen Smale and Robert L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, Third Edition, 2013, Elsevier.
- Steven H. Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, CRC Press, 2018.
- Stephen Lynch, Dynamical Systems with Applications using MATLAB, Second Edition, 2014, Birkhäuser Cham
Name of the tutors:
S.No. | Name | Affiliation |
1 | Dr. Madhukant Sharma | DA-IICT Gandhinagar |
2 | Prof. Syed Abbas | IIT Mandi |
3 | Dr. Mukesh Tiwari | DA-IICT Gandhinagar |
Time Table
Date, Days | Lecture 1 9:30- 11:00 |
11:00 - 11:30 | Lecture 2 11:30- 01:00 |
1:00 | Lecture 3 2:30-3:30 |
3:30 - 4:00 | Tutorial 1 4:00- 5:00 |
5:00-5:30 |
(Speaker’s name) | Tea | (Speaker’s name) | Lunch | (Speaker’s name) | Tea | (Tutor’s name) | Snacks | |
04-01-2025 Saturday |
MS | SA | MS | MS, SA, MT | ||||
05-01-2025 Sunday |
MT | MT | MS | MS, SA, MT | ||||
06-01-2025 Monday |
MT | SA | MT | MS, SA, MT | ||||
07-01-2025 Tuesday |
MS | SA | MS | MS, SA, MT | ||||
08-01-2025 Wednesday |
MT | SA | MT | MS, SA, MT | ||||
09-01-2025 Thursday |
MT | MT | MS | MS, SA, MT | Valedictory Session |
Full forms for the abbreviations of speakers and tutors:
- Prof. Syed Abbas (SA) https://faculty.iitmandi.ac.in/~abbas/
- Dr. Mukesh Tiwari (MT) https://www.daiict.ac.in/faculty/mukesh-tiwari
- Dr. Madhukant Sharma (MS) https://www.daiict.ac.in/faculty/madhu-kant-sharma