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DTSTAMP:20250512T233836Z
DESCRIPTION:“When slow meets global: geometric insight from numerics”\n\nHi
 nke Osinga\, University of Auckland (joint work with José Mujica (Valparaí
 so) and Bernd Krauskopf (Auckland))\n\nTuesday\, September 11\, 12-1pm\n\n
 McIntyre Building\, Room 1027\n\nAbstract: Global manifolds are the backbo
 ne of a dynamical system and key to the characterisation of its behaviour.
  They arise in the classical sense of invariant manifolds associated with 
 saddle-type equilibria or periodic orbits and also in the form of finite-t
 ime invariant manifolds in systems that evolve on multiple time scales. Th
 e latter are known as slow manifolds\, because the flow along such manifol
 ds is very slow compared with the rest of the dynamics. Slow manifolds are
  known to organize the number of small oscillations of so-called mixed-mod
 e oscillations (MMOs). Their interactions with global invariant manifolds 
 produce complicated dynamics about which only little is known from a few e
 xamples in the literature. Both global and slow manifolds need to be compu
 ted numerically. We developed accurate numerical methods based on two-poin
 t boundary value problem continuation\, which have the major advantage tha
 t they remain well posed in parameter regimes where the time-scale separat
 ion varies. These techniques are particularly useful when studying changes
  in the global system dynamics\, such as MMOs\, global re-injection mechan
 isms\, transient bursting\, and phase sensitivity. This talk will focus on
  a transition through a quadratic tangency between the global unstable man
 ifold of a saddle-focus equilibrium and a repelling slow manifold in a slo
 w-fast system at the onset of MMO behaviour\; more precisely\, just as the
  equilibrium undergoes a supercritical singular Hopf bifurcation. We descr
 ibe the local and global properties of the manifolds\, as well as the role
  of the interaction as an organizer of large-amplitude oscillations in the
  dynamics. We find and discuss recurrent dynamics in the form of MMOs\, wh
 ich can be continued in parameters to Shilnikov homoclinic bifurcations.”
 \n
DTSTART:20180911T160000Z
DTEND:20180911T170000Z
LOCATION:Room 1027\, McIntyre Medical Building\, CA\, QC\, Montreal\, H3G 1
 Y6\, 3655 promenade Sir William Osler
SUMMARY:Seminar Series in Quantitative Life Sciences and Medicine
URL:/qls/channels/event/seminar-series-quantitative-li
 fe-sciences-and-medicine-289418
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