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Zbl 0542.34043
Hutson, V.
A theorem on average Liapunov functions. (English)
[J] Monatsh. Math. 98, 267-275 (1984). ISSN 0026-9255; ISSN 1436-5081/e

For a system of ordinary differential equations, {\it J. Hofbauer} [ibid. 91, 233-240 (1981; Zbl 0449.34039)] gave a criterion, framed in terms of an 'average' Lyapunov function, for a compact set to be a repeller (in a certain strong sense). From the point of view of applications this criterion is extremely useful, as it is often considerably easier to find an average Lyapunov function than a Lyapunov function in the usual sense. The aim of this paper is to increase the range of applicability of Hofbauer's result by removing certain unnecessary technical restrictions. Our result is illustrated by applying it to prove a rather strong coexistence criterion for an ecological system.

MSC 2000:: *34D20 Lyapunov stability of ODE
92D25 Population dynamics

Keywords: Lyapunov function; repeller; ecological system

Citations: Zbl 0449.34039

Cited in: Zbl 0871.92023

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