Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 32, Issue 5, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127422500651
Keywords
Kolmogorov system; Lotka-Volterra system; phase portrait; Poincare disc
Funding
- Ministerio de Ciencia e Innovacion, Agencia Estatal de Investigacion (Spain) [PID2020-115155GB-I00]
- Conselleria de Educacion, Universidade e Formacion Profesional (Xunta de Galicia) [ED431C 2019/10]
- FEDER
- Ministerio de Educacion, Cultura y Deporte de Espana [FPU17/02125]
- Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigacion Grant [PID2019104658GB-I00]
- Agencia de Gestio d'Ajuts Universitaris i de Recerca Grant [2017SGR1617]
- H2020 European Research Council Grant [MSCARISE-2017-777911]
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This paper classifies the five-parameter planar Kolmogorov systems and provides a topological classification of their phase portraits on the Poincare disc. The study reveals that these systems have 13 topologically distinct global phase portraits.
We classify the global dynamics of the five-parameter family of planar Kolmogorov systems (y)over dot = y(b(0) + b(1yz) + b(2y) + b(3z)), (z)over dot = z(c(0) + b(1yz) + b(2y) + b(3z)), which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at inifnity. We give the topological classification of their phase portraits in the Poincare disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.
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