A discrete-time model for cryptic oscillations in predator-prey systems
type: Item
instance of: scholarly article
title: A discrete-time model for cryptic oscillations in predator-prey systems
zbMATH Open document ID: 1186.37107
published in: Physica D
publication date: 2009-12-16T00:00:00Z
review text: The notion of ``\textit{cryptic oscillations in predator-prey systems}'' defines a situation when -- in such systems of the predator-prey type -- the predator population oscillates widely while the total prey population has only small-amplitude oscillations in phase opposition to those of the predator. Two models are proposed:{ \parindent5mm \begin{itemize}\item[1.] A general model (Section 2), using two prey species with different palatability and one predator species. It is described in continuous, discrete and ultra discrete (cellular automaton) forms, with some numerical simulations for pointing out the phenomenon of cryptic oscillations. \item[2.] An improved model (Section 4), focused on the description of the transient phase of predator-prey oscillations, when some chaotic bursts recur periodically. The authors' opinion is ``\textit{these bursts are most probably a feature of the model used and do not necessarily correspond to a behavior of the real system}''. \end{itemize}} The paper is interesting, easy to be followed, pedagogically constructed. All information is described in detail, and many examples are provided. Personally I did not understood the importance of the cellular automata in the construction of both models, because only the first two variants are analysed and used in the simulations.
reviewed by: Adrian Atanasiu
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 37B15
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 68Q80
zbMATH DE Number: 5648721
zbMATH Keywords: predator-prey systems
zbMATH Keywords: discrete-time models
zbMATH Keywords: ecological coupling
zbMATH Keywords: cryptic oscillations
zbMATH Keywords: cellular automata
Wikidata QID: Q115567784
author: R. Willox
author: A. Ramani
author: B. Grammaticos
MaRDI profile type: Publication
full work available at URL: j.physd.2009.09.007
OpenAlex ID: W2149927416
cites work: Q4274312
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cites work: Discretization-induced delays and their role in the dynamics
cites work: Q5792555
cites work: A Generalization of a Theorem of Bôcher
cites work: Effects of rapid prey evolution on predator-prey cycles
DOI: 10.1016/J.PHYSD.2009.09.007
description: scientific article; zbMATH DE number 5648721