Cookies

We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Biomathematics Seminar: Spiralling patterns in models inspired by bacterial games with cyclic competition

Presented by Mauro Mobilia, Leeds University

20 January 2015 14:00 in CM105

Evolutionary game theory, where the success of one species depends on what the others are doing, provides a promising framework
to investigate the mechanisms allowing the maintenance of biodiversity. Experiments on microbial populations have shown that cyclic
local interactions promote species coexistence. In this context, rock-paper-scissors games are used to model populations in cyclic
competition. After a brief overview of some inspiring experiments, I will discuss the subtle interplay between the individuals'
mobility and local interactions in two-dimensional rock-paper-scissors systems. This leads to the loss of biodiversity above a
certain mobility threshold, and to the formation of spiralling patterns below that threshold. I will then discuss a generic
rock-paper-scissors metapopulation model formulated on a two-dimensional grid of patches. When these have a large carrying capacity,
the model's dynamics is faithfully described in terms of the system's complex Ginzburg-Landau equation suitably derived from a
multiscale asymptotic expansion. The properties of the ensuing complex Ginzburg-Landau equation are exploited to derive the
system's phase diagram and to characterize the spatio-temporal properties of the spiralling patterns in each phase. This enables
us to analyse the spiral waves stability, the influence of linear and nonlinear diffusion, and the far-field breakup of the
spiralling patterns.

Contact christopher.prior@durham.ac.uk for more information