skip to content

Spiralling patterns in models inspired by bacterial games with cyclic competition

Presented by: 
M Mobilia University of Leeds
Tuesday 25th November 2014 - 15:00 to 16:00
INI Seminar Room 2
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 the survey 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 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 pattern.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons