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The discrete dynamics of monotonically decomposable maps. (English) Zbl 1118.65057
J. Math. Biol. 53, No. 4, 747-758 (2006); erratum ibid. 57, No. 2, 309-310 (2008).
Summary: We extend results of J.-L. Gouzé and K. P. Hadeler [Nonlinear World 1, 23–34 (1994; Zbl 0803.65076)] concerning the dynamics generated by a map on an ordered metric space that can be decomposed into increasing and decreasing parts. Our main results provide sufficient conditions for the existence of a globally asymptotically stable fixed point for the map. Applications to discrete-time, stage-structured population models are given.

MSC:
65J15 Numerical solutions to equations with nonlinear operators
47H10 Fixed-point theorems
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
92D25 Population dynamics (general)
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