NON-AUTOMOUS DISCRETE DYNAMICAL SYSTEMS. AND APPLICATIONS TO BIOLOGY

[TMCSC]

July 10, 2019  15:40-16:40

四川大学东三教学楼 247

[lecture]0710Saber Elaydi-01.jpg

SPEAKER

Saber Elaydi (Trinity University)

ABSTRACT

We consider a discrete non-autonomous semi-dynamical system generated by a family of continuous maps defined on a locally compact metric space. It is assumed that this family of maps uniformly converges to a continuous map. Such a non-autonomous system is called an asymptotically autonomous system.  We extend the dynamical system to the metric one-point compactification of the phase space. Our study will be applied to a special class of maps, triangular maps. This is done via the construction of an associated skew-product dynamical system. We prove, among other things, that the omega limit sets are invariant and invariantly connected. We apply our results to three populations models, the Ricker model with no Allee effect, Elaydi-Sacker model with the Allee effect, and the 2-species hierarchical competition Ricker model with the Allee effect, where it is assumed that the reproduction rates change with time due to habitat fluctuation.

ORGANIZERS

洪绍方（四川大学）

寇     辉（四川大学）

连     增（四川大学）

SUPPORTED BY

国家天元数学西南中心

四川大学数学学院