Mathematics & Statistics Departmental Research Seminar

Tracking travelling waves in rough and random environments

Abstract:

Travelling waves appear in a wide variety of physical and biological systems that change over space and time. If the laws describing the evolution of a system exhibiting travelling waves are assumed to be deterministic, then one can use relatively well-established ODE techniques to study the profile and speed of a wave. However, many systems exhibiting travelling waves are, in fact, under the constant influence of small amplitude, high frequency, random perturbations. Even when these random perturbations are small, it is known that they may have a large effect on the behaviour of travelling waves.

In this talk, we provide a high level survey of some techniques for understanding the effects of these perturbations on the speed and profile of travelling waves. As examples, will also discuss the application of these techniques to models from mathematical physiology, including the FitzHugh-Nagumo system and neural field equations.