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Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system
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UNSPECIFIED (2003) Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system. NONLINEARITY, 16 (4). pp. 1277-1293. ISSN 0951-7715.
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Abstract
Lotka-Volterra systems have been extensively studied by many authors, both in the autonomous and non-autonomous cases. In previous papers the time asymptotic behaviour as t --> infinity has been considered. In this paper we also consider the 'pullback' asymptotic behaviour which roughly corresponds to observing a system 'now' that has already been evolving for a long time. For a competitive system that is asymptotically autonomous both as t --> -infinity and as t --> +infinity we show that these two notions of asymptotic behaviour can be very different but are both important for a full understanding of the dynamics. In particular there are parameter ranges for which, although one species dies out as t --> infinity, there is a distinguished time-dependent coexistent state that is attracting in the pullback sense.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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Journal or Publication Title: | NONLINEARITY | ||||
Publisher: | IOP PUBLISHING LTD | ||||
ISSN: | 0951-7715 | ||||
Official Date: | July 2003 | ||||
Dates: |
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Volume: | 16 | ||||
Number: | 4 | ||||
Number of Pages: | 17 | ||||
Page Range: | pp. 1277-1293 | ||||
Publication Status: | Published |
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