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Estimates of size of cycle in a predator-prey system
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2018 (English)In: Differential Equations and Dynamical Systems, ISSN 0971-3514, E-ISSN 0974-6870Article in journal (Refereed) Epub ahead of print
Abstract [en]

We consider a Rosenzweig–MacArthur predator-prey system which incorporates logistic growth of the prey in the absence of predators and a Holling type II functional response for interaction between predators and preys. We assume that parameters take values in a range which guarantees that all solutions tend to a unique limit cycle and prove estimates for the maximal and minimal predator and prey population densities of this cycle. Our estimates are simple functions of the model parameters and hold for cases when the cycle exhibits small predator and prey abundances and large amplitudes. The proof consists of constructions of several Lyapunov-type functions and derivation of a large number of non-trivial estimates which are of independent interest.

Place, publisher, year, edition, pages
Springer, 2018.
Keywords [en]
Locating limit cycle, Locating attractor, Size of limit cycle, Lyapunov function, Lyapunov stability
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:umu:diva-153284DOI: 10.1007/s12591-018-0422-xOAI: oai:DiVA.org:umu-153284DiVA, id: diva2:1263399
Available from: 2018-11-15 Created: 2018-11-15 Last updated: 2019-04-05

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Lundström, Niklas

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • rtf