Course Details
Subject {L-T-P / C} : PH6114 : Non – Linear Dynamics, Chaos and Its Recent Applications { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Biplab Ganguli
Syllabus
Geometrical view of solution of differential equations : vector flow in one and two dimensions. Trajectories in phase space and phase portrait. Linear stability theory . Limit cycle attractor and its existence. Theory and types of bifurcation in one, two and higher dimensions. 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. Numerical methods to calculate Lyapunov exponent, Poincare map and bifurcation diagram. Synchronization in coupled systems and network. Introduction to quantum chaos.
Course Objectives
- 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
Course Outcomes
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.
Essential Reading
- D.W.Jordan & P.Smith, Nonlinear Ordinary Differential Equations, Oxford
- Steven H. Strogatzt, Nonlinear Dynamics and Chaos, Westview Press
Supplementary Reading
- Robert C. Hilborn, Chaos and Nonlinear Dynamics, Oxford
- Sandro Wimberger, Nonlinear Dynamics & Quantum Chaos, Springer