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Strongly order preserving semiflows generated by functional differential equations. (English) Zbl 0735.34065

The authors’ goal is to extend some of their previous results in the theory of monotone dynamical systems to certain systems of functional differential equations. The fundamental paper in this field was written by M. Hirsch and appeared in 1988; Hirsch established that most orbits of a strongly monotone semiflow on a strongly ordered space tend to a set of equilibria. The authors previously introduced the quasimonotone property for functional differential equations. However, this property is quite restrictive, and, in many interesting examples, functional differential equations are not quasimonotone.
The aim of the authors here is to weaken the quasimonotone assumption enough to get an open and dense subset of convergent and stable points for interesting systems of functional differential equations. Two specific applications are then considered: the dynamics of a spatially distributed population with a juvenile period, and a cyclic feedback system.

MSC:

34K30 Functional-differential equations in abstract spaces
37-XX Dynamical systems and ergodic theory
92D25 Population dynamics (general)
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