Syllabus

Module-I :Geometrical view of solution of differential equations : vector flow in one and two dimensions. Trajectories in phase space and phase portrait.

Module-II : Linear stability theory . Limit cycle attractor and its existence.

Module-III : Theory and types of bifurcation in one, two and higher dimensions. Poincare map and bifurcation diagram.

Module-IV : Strange attractor in three and higher dimensions and theory of chaotic dynamics. Difference equations and maps. Route to chaos via period doubling. Fractal and fractal dimension. Lyapunov exponent and its numerical methods of calculations

Module-V : Synchronization in coupled systems and network.

Module-VI Introduction to quantum chaos.

To introduce this new and modern theory of non-linear phenomena, generally not included in traditional course structure and which is mostly unknown to postgraduate students.

This course particularly useful to address real problems which are in general non-linear and could be studied under approximation by the theories applicable for linear systems.

It is an interdisciplinary course and so would serve a wider audience.

This course introduces many complex systems like network in biological systems, electronic circuits.

1. The course would facilitate researchers, working in diverse fields of science and engineering and dealing with complex systems, to quantify nature of dynamics arising out of non-linearity.
2. This course would help students to explore interdiscipilinary avenue for further studies.
3. Stusents would learn many numerical techniques which are specifically designed for non-linear differential equations.
4. Students will learn alternative methods of obtaining qualitative results using geometrical methods, than using traditional quantitative result.
5. Students would learn applications of this new theory in diverse fields.

D.W.Jordan & P.Smith, Nonlinear Ordinary Differential Equations, Oxford

Steven H. Strogatzt, Nonlinear Dynamics and Chaos, Westview Press

Robert C. Hilborn, Chaos and Nonlinear Dynamics, Oxford

Sandro Wimberger, Nonlinear Dynamics & Quantum Chaos, Springer