Chaotic attractors in Atkinson-Allen model of four competing species

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http://hdl.handle.net/10138/318561

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Gyllenberg , M , Jiang , J & Niu , L 2020 , ' Chaotic attractors in Atkinson-Allen model of four competing species ' , Journal of biological dynamics , vol. 14 , no. 1 , pp. 440-453 . https://doi.org/10.1080/17513758.2020.1779828

Title: Chaotic attractors in Atkinson-Allen model of four competing species
Author: Gyllenberg, Mats; Jiang, Jifa; Niu, Lei
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2020-06-19
Language: eng
Number of pages: 14
Belongs to series: Journal of biological dynamics
ISSN: 1751-3758
URI: http://hdl.handle.net/10138/318561
Abstract: We study the occurrence of chaos in the Atkinson-Allen model of four competing species, which plays the role as a discrete-time Lotka-Volterra-type model. We show that in this model chaos can be generated by a cascade of quasiperiod-doubling bifurcations starting from a supercritical Neimark-Sacker bifurcation of the unique positive fixed point. The chaotic attractor is contained in a globally attracting invariant manifold of codimension one, known as the carrying simplex. Biologically, our study implies that the invasion attempts by an invader into a trimorphic population under Atkinson-Allen dynamics can lead to chaos.
Subject: Atkinson-Allen model
carrying simplex
Neimark-Sacker bifurcation
quasiperiod-doubling bifurcation
chaotic attractor
invasion
LOTKA-VOLTERRA SYSTEM
3 LIMIT-CYCLES
GLOBAL STABILITY
CARRYING SIMPLEX
EQUIVALENT CLASSIFICATION
DIFFERENTIAL-EQUATIONS
DYNAMICS
BOUNDARY
UNIQUENESS
SIMPLICES
111 Mathematics
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