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SUMMARY:Homoclinic snaking and the emergence of localised patterns beyond 
 all asymptotic orders - Edgardo Villar-Sepúlveda (University of Bristol)
DTSTART:20221101T140000Z
DTEND:20221101T145000Z
UID:TALK185195@talks.cam.ac.uk
DESCRIPTION:Joint presentation by Edgardo Villa-Sepulveda and Alan Champne
 ys\, Department of Engineering Mathematics\, University of Bristol. &nbsp\
 ;\nWithin spatially extended pattern formation systems\, so-called snakes 
 and ladders bifurcation diagrams of localised patterns arise within so cal
 led Pomeau pinning regions. These patterns can be understood qualitatively
  using the geometric theory of dynamical systems. In the limit of a certai
 n codimension-two bifurcation Turing bifurcation\, these complex bifurcati
 on diagrams are known to arise within an exponentially thin parameter wedg
 e around a Maxwell equal-energy curve. &nbsp\;In principle\, the coefficie
 nt of this beyond-all-orders envelope can be calculated in specific exampl
 es\, using a theory pioneered by Kozyreff and Chapman for the case of the 
 Swift-Hohenberg equation. The purpose of this talk is to explore how far t
 his theory can be generalised to general pattern formation models\, such a
 s the Schakenberg and Brusselator reaction-diffusion systems. We shall als
 o discuss related beyond-all-orders problems that arise in dynamical syste
 ms\, such as the local birth of chaos from a saddle-node-Hopf bifurcation 
 in low-order dissipative dynamical systems. &nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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