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SUMMARY:Spiralling patterns in models inspired by bacterial games with cyc
 lic competition - Mobilia\, M (University of Leeds)
DTSTART:20141125T150000Z
DTEND:20141125T160000Z
UID:TALK56315@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Evolutionary game theory\, where the success of one species de
 pends on what the others are doing\, provides a promising framework to inv
 estigate the mechanisms allowing the maintenance of biodiversity. Experime
 nts on microbial populations have shown that cyclic local interactions pro
 mote species coexistence. In this context\, rock-paper-scissors games are 
 used to model populations in cyclic competition.\n\nAfter the survey of so
 me inspiring experiments\, I will discuss the subtle interplay between the
  individuals' mobility and local interactions in two-dimensional rock-pape
 r-scissors systems. This leads to the loss of biodiversity above a certain
  mobility threshold\, and to the formation of spiralling patterns below th
 at threshold. I will then discuss a generic rock-paper-scissors metapopula
 tion model formulated on a two-dimensional grid of patches. When these hav
 e a large carrying capacity\, the model's dynamics is faithfully described
  in terms of the system's complex Ginzburg-Landau equation suitably derive
 d from a multiscale expansion. The properties of the ensuing complex Ginzb
 urg-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\, th
 e influence of linear and nonlinear diffusion\, and the far-field breakup 
 of the spiralling pattern.\n
LOCATION:Seminar Room 2\, Newton Institute Gatehouse
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