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:

  1. 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
  2. Morris W. Hirsch, Stephen Smale and Robert L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, Third Edition, 2013, Elsevier.
  3. Steven H. Strogatz, Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry, and Engineering, CRC Press, 2018.
  4. 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:

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