On a boom and bust year class cycle

Odo Diekmann, Natalia Davydova, Stephanus A. van Gils

Research output: Contribution to journalArticleAcademicpeer-review

18 Citations (Scopus)

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 languageUndefined
Pages (from-to)327-335
Number of pages9
JournalJournal of difference equations and applications
Volume4
Issue number5
DOIs
Publication statusPublished - 4 Apr 2005

Keywords

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

Cite this

Diekmann, Odo ; Davydova, Natalia ; van Gils, Stephanus A. / On a boom and bust year class cycle. In: Journal of difference equations and applications. 2005 ; Vol. 4, No. 5. pp. 327-335.
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On a boom and bust year class cycle. / Diekmann, Odo; Davydova, Natalia; van Gils, Stephanus A.

In: Journal of difference equations and applications, Vol. 4, No. 5, 04.04.2005, p. 327-335.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Diekmann, Odo

AU - Davydova, Natalia

AU - van Gils, Stephanus A.

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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

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DO - 10.1080/10236190412331335409

M3 - Article

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SP - 327

EP - 335

JO - Journal of difference equations and applications

JF - Journal of difference equations and applications

SN - 1023-6198

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