2006
DOI: 10.1155/ddns/2006/37264
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A short proof of the Cushing‐Henson conjecture

Abstract: We give a short proof of the Cushing-Henson conjecture concerning Beverton-Holt difference equation, which is important in theoretical ecology. The main result shows that a periodic environment is always deleterious for populations modeled by the Beverton-Holt difference equation.

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Cited by 81 publications
(61 citation statements)
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“…The dynamics and properties of both equations have been studied in great detail in recent literature (see, for example [3][4][5][6][9][10][11][12][13][16][17][18][19][20][21][22][23][24][25][26]30,36,39])…”
Section: Introductionmentioning
confidence: 99%
“…The dynamics and properties of both equations have been studied in great detail in recent literature (see, for example [3][4][5][6][9][10][11][12][13][16][17][18][19][20][21][22][23][24][25][26]30,36,39])…”
Section: Introductionmentioning
confidence: 99%
“…The first and second equalities of (13) show that the trace of the product is the product of the traces, thus it follows by (12) and (13) that the leading coefficient of trðMÞ is Q k j¼1 ðF n j þ1 À F n j Þ ¼ F n 1 À1 F n 2 À1 . .…”
Section: Auxiliary Resultsmentioning
confidence: 97%
“…Especially, the periodic property of difference equations or systems had been widely investigated, such as [10][11][12][13][14][15][16][17]. Mathematically, the subsystems of a switched system are often depicted by a collection of indexed differential or difference equations.…”
Section: Introductionmentioning
confidence: 99%
“…A large number of papers dealing with such or related equations have been published (see, e.g, [6,16,[22][23][24]). In [34], the following model incorporating litter inhibition is discussed:…”
Section: Introductionmentioning
confidence: 99%