On a boom and bust year class cycle

Odo Diekmann; Natalia Davydova; Stephanus A. van Gils

doi:10.1080/10236190412331335409

On a boom and bust year class cycle

Odo Diekmann
, Natalia Davydova
, Stephanus A. van Gils

Research output: Contribution to journal › Article › Academic › peer-review

20 Citations (Scopus)

6 Downloads (Pure)

Abstract

We motivate and describe a class of nonlinear Leslie matrix models for semelparous populations, like cicadas and Pacific salmon. We then focus on a Cushing-inspired special case for which one can show rigorously that a heteroclinic boundary cycle exists and attracts nearby orbits for a certain range of parameters. Along the way we formulate some open problems concerning a carrying simplex and global behaviour.

Original language	Undefined
Pages (from-to)	327-335
Number of pages	9
Journal	Journal of difference equations and applications
Volume	4
Issue number	5
DOIs	https://doi.org/10.1080/10236190412331335409
Publication status	Published - 4 Apr 2005

Keywords

Heteroclinic cycle
METIS-226013
Leslie matrix model
IR-74623
Semelparous species
EWI-13996

Access to Document

10.1080/10236190412331335409

http://eprints.eemcs.utwente.nl/secure2/13996/01/Diekmann_05_On-a-boom-and-bust-year-class-cycle.pdf

Cite this

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title = "On a boom and bust year class cycle",

abstract = "We motivate and describe a class of nonlinear Leslie matrix models for semelparous populations, like cicadas and Pacific salmon. We then focus on a Cushing-inspired special case for which one can show rigorously that a heteroclinic boundary cycle exists and attracts nearby orbits for a certain range of parameters. Along the way we formulate some open problems concerning a carrying simplex and global behaviour.",

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AU - Davydova, Natalia

AU - van Gils, Stephanus A.

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N2 - We motivate and describe a class of nonlinear Leslie matrix models for semelparous populations, like cicadas and Pacific salmon. We then focus on a Cushing-inspired special case for which one can show rigorously that a heteroclinic boundary cycle exists and attracts nearby orbits for a certain range of parameters. Along the way we formulate some open problems concerning a carrying simplex and global behaviour.

AB - We motivate and describe a class of nonlinear Leslie matrix models for semelparous populations, like cicadas and Pacific salmon. We then focus on a Cushing-inspired special case for which one can show rigorously that a heteroclinic boundary cycle exists and attracts nearby orbits for a certain range of parameters. Along the way we formulate some open problems concerning a carrying simplex and global behaviour.

KW - Heteroclinic cycle

KW - METIS-226013

KW - Leslie matrix model

KW - IR-74623

KW - Semelparous species

KW - EWI-13996

U2 - 10.1080/10236190412331335409

DO - 10.1080/10236190412331335409

M3 - Article

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