PH4273 / PH6423 :  Nonlinear Dynamics
(August 2026 semester)

This is a first course on nonlinear dynamics meant for students from all disciplines with a background in calculus and linear algebra.

Course contents : ∙ Download as PDF file

• Linear and nonlinear systems in 1D
• Bifurcations in 1D
• Flows on a circle
• Linear and nonlinear systems in 2D
• Bifurcations in 2D
• Symbolic sequences
• Characterisation of chaos
• chaos in 1D maps and flows
• Measures of chaos and routes to chaos
• Hamiltonian chaos
• Generalised dimensions, fractals and strange attractors

Books :
(Reference numbers mentioned later refer to these books.)

1. Nonlinear dynamics and chaos by Steven Strogatz
(Classic introductory text for students from any science background.)

2. Chaos : Introduction to dynamical systems by K. T. Alligood, T. D. Sauer and J. A. Yorke
(This textbook has mathemtical flavour to it.)

3. Chaos in dynamical systems  by Edward Ott
(The chaos textbook for physicists. A bit too condensed and fast-paced.)

4. Differential equations, dynamical systems and an introduction to chaos  by M. W. Hirsch, Stephen Smale and Robert Devaney
(Good for the chaos part)

5. Chaos and nonlinear dynamics : An introduction for scientists and engineers by Robert Hilborn
(A good nonlinear dynamics textbook for physicists. Good for those seeking physical intuition and explanations.)

Evaulation :

Quiz (1 or 2)	: 30%
Midsem	: 30%
Endsem	: 40%

║ 31.8.2026 ║ Lecture 8 ║

Flows on a circle. Saddle-node bifurcation and passage through bottleneck region, square-root scaling law in the vicinity of saddle-node bifurcation.

║ 25.8.2026 ║ Lecture 7 ║

Bead in a rotating hoop. Example of pitchfork bifurcation, non-dimensionalising the equation of motion.

║ 24.8.2026 ║ Lecture 6 ║

Bifurcations (Continued)

║ 18.8.2026 ║ Lecture 5 ║

Bifurcations. Transcritical and pitchfork bifurcation. Stabilising unstable systems. Hysterisis. What all this means in practice ? ▶ Additional readings if you are interested (not mandatory for the course) : Anticipating critical transitions Pitchfork bifurcation and critical temperature transition

║ 17.8.2026 ║ ║

Class cancelled.

║ 11.8.2026 ║ Lecture 4 ║

Flows in one dimension. Figuring out solution without actually solving them. Existence and uniqueness of solutions for ODEs.

║ 10.8.2026 ║ Lecture 3 ║

Nonlinear oscillators, separatrix, time-period, calculating time-period of oscillatory motion.

║ 4.8.2026 ║ Lecture 2 ║

Nonlinear systems. Exact solution of linear and nonlinear pendulum in terms of elliptic functions. Time-period of oscillation. ▶ Nonlinear pendulum : Comprehensive solution, and one more resource for analytical solution.

║ 3.8.2026 ║ Lecture 1 ║

Introduction to nonlinearity. Effects of nonlinearity (e.g, Millenium bridge collapse), synchronisation, basics. Additional reading (not mandatory for the course) : A research articleon this bridge collapse

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