Venue: Emmy Noether Seminar Room
Class Timings: Wednesdays and Fridays 3:30 PM to 5:00 PM
First Meeting: 9 January 2026 (Friday)
Course Description: This course introduces nonlinear dynamical systems (including flows, maps, attractors, bifurcations, collective dynamics, and chaos) with motivating applications drawn from neuroscience. Core concepts in dynamical systems theory are explored through examples across multiple neural scales, from single neurons to population-level activity. The course combines theoretical analysis with computational modelling and simulation.
No prior background in biology is assumed, but a basic understanding of linear algebra, ordinary differential equations, and programming is required. Students may use any programming language, though Python will be preferred.
Course Syllabus: This course introduces nonlinear dynamical systems (including flows, maps, attractors, bifurcations, collective dynamics, and chaos) with motivating applications drawn from neuroscience. Core concepts in dynamical systems theory are explored through examples across multiple neural scales, from single neurons to population-level activity. The course combines theoretical analysis with computational modelling and simulation.
Detailed syllabus: TBA.
Course Outcome: At the end of the course, a student should be able to:
(1) Analyse low-dimensional dynamical systems qualitatively and quantitatively.
(2) Classify and compute local bifurcations.
(3) Analyse the collective dynamics of interacting systems through perspectives of synchronization.
(4) Formulate dynamical systems models of neural phenomena across multiple length and time scales.
(5) Critically read and interpret neuroscience papers that use dynamical systems language, connecting biological descriptions with mathematical formalism.
References: Textbooks and reference books:
(1) Nonlinear Dynamics and Chaos - Steven Strogatz
(2) Chaos in Dynamical Systems - Edward Ott
(3) Dynamical Systems in Neuroscience - Eugene M. Izhikevich
(4) Mathematical Foundations of Neuroscience - Bard Ermentrout and David Terman
(5) Theoretical Neuroscience - Peter Dayan and Larry Abbott
Course Evaluation : Assignments + Class presentation. Break-up TBA