Limit cycles of a cubic Kolmogorov system
type: Item
instance of: scholarly article
title: Limit cycles of a cubic Kolmogorov system
zbMATH Open document ID: 0858.34023
DOI: 10.1016/0893-9659(95)00095-X
published in: Applied Mathematics Letters
publication date: 1997-03-31T00:00:00Z
review text: The authors consider limit cycles which bifurcate from a critical point in case of cubic Kolmogorov systems of the form \[ \dot x=x(x-2y+2)(Ax+y+B),\quad \dot y=y(2x-y-2)(Dx+y+C).\tag{1} \] The authors use the computer algebra procedure FINDETA which was described by the first two authors [J. Symb. Comput. 9, No. 2, 215-224 (1990; Zbl 0702.68072)] to compute the focal values at the critical point \((2,2)\) and show that for certain cubic Kolmogorov systems (1), four and not more than four limit cycles can bifurcate from a critical point in the first quadrant; moreover, three fine foci of order one can coexist and a limit cycle can bifurcate from each.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 915050
zbMATH Keywords: limit cycles
zbMATH Keywords: cubic Kolmogorov systems
zbMATH Keywords: computer algebra procedure FINDETA
zbMATH Keywords: focal values
zbMATH Keywords: fine foci
author: Noel G. Lloyd
author: Jane M. Pearson
author: Eduardo Sáez
author: Ivan Szanto
reviewed by: Lansun Chen
MaRDI profile type: Publication
cites work: Systems of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems
cites work: Q3729336
cites work: REDUCE and the bifurcation of limit cycles
cites work: Algorithmic Derivation of Centre Conditions
full work available at URL: 0893-9659(95)00095-x
OpenAlex ID: W2069274758
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description: scientific article; zbMATH DE number 915050