General Information

Mathematical models of phenomena in the physical sciences or processes in the engineering and biological sciences invariably take the form of nonlinear dynamical systems and partial differential equations (PDEs). The expertise of the Nonlinear Dynamics and Applied PDEs group lies in attacking these systems with the modern techniques of applied mathematics, such as symmetry and asymptotic methods coupled with numerical explorations and dynamical systems theory. Occasionally the goal is to understand the creation of patterns from otherwise featureless background states, or the onset of new dynamical behaviour (such as synchrony in populations of coupled oscillators). But the mathematics involved in these problem is often of equal interest, entailing novel twists and turns in the application of mathematical technology, and motivating the development of new techniques or adaptations of existing ones. Gray-Scott model in a square domain: self-replication of a localised stripe pattern, followed by the breakup of the stripe into a zigzag instability and then into localised spots

Patterns in the Gray-Scott reaction-diffusion model in a square domain: the evolution of an initial triangle depends sensitively on the model parameters

Core Faculty

The Nonlinear Dynamics & Applied PDEs Group is composed of several core IAM faculty who are actively involved in the IAM activities and supervise IAM students or postdoctoral fellows. We are always interested to hear from potential students or fellows with background in mathematics, physics or engineering. We often supervise undergraduate thesis projects and take on summer research undergraduate students. Candidates interested in research in Nonlinear Dynamics & Applied PDEs in the IAM are encouraged to contact one or more of the core faculty as potential supervisors and let them know of their interests.

Recommended Courses

Courses given by IAM faculty provide the foundation for research in Nonlinear Dynamics & Applied PDEs, as well as outlining the essential tools which comprise the classical and modern techniques of Applied Mathematics.

Sample Publications

Listed below are some of the recent theses and journal publications by IAM students, IAM faculty, IAM postdoctoral fellows and IAM alumni in the field of Nonlinear Dynamics & Applied PDEs. Click on the item of interest to open a thesis file, an article pdf on the author's web page, or an article abstract on the journal site.