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SUMMARY:E. Cabral Balreira (Trinity University)
DTSTART:20221112T190000Z
DTEND:20221112T200000Z
DTSTAMP:20260423T035542Z
UID:Dynamics/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Dynamics/12/
 ">Geometric ideas on global stability and monotonicity for discrete system
 s</a>\nby E. Cabral Balreira (Trinity University) as part of Little school
  dynamics\n\n\nAbstract\nIt is an important problem in discrete dynamics t
 o\ndetermine when local stability of fixed points implies global\nstabilit
 y. We will focus on the planar Ricker competition model and\nintroduce ide
 as from singularity theory to describe the dynamics of\nthe images of the 
 critical curves to show that local stability of the\ncoexistence (positive
 ) fixed point implies global stability. The\nintroduction of geometric met
 hods will allow us to revisit the notion\nof monotonicity and develop a ge
 ometric generalization for the notion\nof monotonicity (or competitive) ma
 ps in higher dimensions. We show\nthat this definition is equivalent for k
 nown results for planar maps\nand provide analytic conditions to check for
  geometric monotonicity\nand global stability. We illustrate our results w
 ith the Beverton-Holt\nand Ricker competition map.\n
LOCATION:https://researchseminars.org/talk/Dynamics/12/
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