TY - JOUR
T1 - Planar Kolmogorov Systems with Infinitely Many Singular Points at Infinity
AU - Diz-Pita, Érika
AU - Llibre, Jaume
AU - Otero-Espinar, M. Victoria
N1 - Publisher Copyright:
© 2022 World Scientific Publishing Company.
PY - 2022/4/1
Y1 - 2022/4/1
N2 - We classify the global dynamics of the five-parameter family of planar Kolmogorov systems C = y(b0 + b1yz + b2y + b3z),ż = z(c0 + b1yz + b2y + b3z), 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 Poincaré disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.
AB - We classify the global dynamics of the five-parameter family of planar Kolmogorov systems C = y(b0 + b1yz + b2y + b3z),ż = z(c0 + b1yz + b2y + b3z), 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 Poincaré disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.
KW - Kolmogorov system
KW - Lotka-Volterra system
KW - Poincaré disc
KW - phase portrait
UR - https://www.scopus.com/pages/publications/85129295161
U2 - 10.1142/S0218127422500651
DO - 10.1142/S0218127422500651
M3 - Article
AN - SCOPUS:85129295161
SN - 0218-1274
VL - 32
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
IS - 5
M1 - 2250065
ER -