期刊
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
卷 31, 期 13, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127421502011
关键词
Kolmogorov system; Lotka-Volterra system; phase portrait; Poincare disc
资金
- Ministerio de Economia, Industria y Competitividad, Agencia Estatal de Investigacion (Spain) (European FEDER support included, UE) [MTM2016-79661-P]
- Conselleria de Educacion, Universidade e Formacion Profesional (Xunta de Galicia) [ED431C 2019/10]
- FEDER funds
- Ministerio de Educacion, Cultura y Deporte de Espana [FPU17/02125]
- Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigacion (FEDER) [PID2019-104658GB-100]
- Agencia de Gestio d'Ajuts Universitaris i de Recerca grant [2017SGR1617]
- H2020 European Research Council [MSCA-RISE-2017-777911]
This paper classifies the phase portraits of all Kolmogorov systems in the Poincare disc, showing that there are 52 topologically distinct phase portraits. These systems are derived from a general three-dimensional Lotka-Volterra system and have a specific Darboux invariant.
In this paper, we classify the phase portraits in the Poincare disc of all the Kolmogorov systems (y) over dot = y(b(0) + b(1)yz + b(2)y + b(3)z), (z) over dot = z(c(0) - mu(b(1)yz + b(2)y + b(3)z)), which depend on six parameters. We prove that these systems have 52 topologically distinct phase portraits in the Poincare disc. These systems are provided by a general three-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = x(i)y(j)z(k), restricted to each surface H(x,y,z) = h varying h is an element of Double-struck capital R, with the additional assumption that they have a Darboux invariant of the form y(l)z(m)e(st).
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