PHY 342 : Nonlinear Dynamics
(January - April, 2012)
This is the first course on nonlinear dynamics.
Course
contents :
Linear and nonlinear systems in 1D
Bifurcations in 1D
Flows on a circle
Linear and nonlinear systems in 2D
Bifurcations in 2D
chaos in 1D maps and flows
Measures of chaos and routes to chaos
Hamiltonian chaos
Dimensions, fractals and strange attractors
Books :
Nonlinear dynamics and chaos by Steven Strogatz
Chaos : Introduction to dynamical systems by K. T. Alligood, T. D. Sauer and J. A. Yorke
Chaos in dynamical systems by Edward Ott
Chaos and nonlinear dynamics : An introduction for scientists and engineers by Robert Hilborn
Introduction to nonlinear physics by Liu Lam
Evaulation :
Class tests / Seminar / Assignments : 30 %
Midsem : 30 %
Final : 40 %
Test 1 (16.2.2012) : Question paper
Solutions to Test 1
Mid-semester exam (29.2.2012) : Question paper
Solutions to Mid-sem exam
Test 3 (12.4.2012) : Questions and solutions
External resources : Chaos course of Prof. Michael Cross
Lecture 1 : Introduction to nonlinearity
Lecture 2 : Linear system, fixed points and generalisation
Lecture 3 : Linear stability analysis for 1D nonlinear system
Lecture 4 : Bifurcations in 1D
Lecture 5 : Flows on circle
Lecture 6 : Flows on circle (contd.)
Lecture 7 : Special lecture on excitable systems
(This will be updated sometime soon.)