Extinction or coexistence in periodic Kolmogorov systems of competitive type

Isabel Coelho; Carlota Rebelo; Elisa Sovrano

doi:10.3934/dcds.2021094

Article Contents

2021, Volume 41, Issue 12: 5743-5764. Doi: 10.3934/dcds.2021094 open access

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Extinction or coexistence in periodic Kolmogorov systems of competitive type

1.
Centro de Matemática Computacional e Estocástica, Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emídio Navarro, 1, 1950-062 Lisboa, Portugal
2.
Centro de Matemática Computacional e Estocástica, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edificio C6, piso 2, 1749-016, Lisboa, Portugal
3.
École des Hautes Études en Sciences Sociales, Centre d'Analyse et de Mathématique Sociales (CAMS), CNRS, 54 Boulevard Raspail, 75006, Paris, France

^* Corresponding author: C. Rebelo
^* Corresponding author: C. Rebelo

Received: March 2021

Revised: May 2021

Early access: June 2021

Published: December 2021

I. Coelho and C. Rebelo have been supported by FCT projects UIDB/04621/2020 and UIDP/04621/2020 of CEMAT at FC-Universidade de Lisboa. E. Sovrano has been supported by the Fondation Sciences Mathématiques de Paris (FSMP)

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Abstract

We study a periodic Kolmogorov system describing two species nonlinear competition. We discuss coexistence and extinction of one or both species, and describe the domain of attraction of nontrivial periodic solutions in the axes, under conditions that generalise Gopalsamy conditions. Finally, we apply our results to a model of microbial growth and to a model of phytoplankton competition under the effect of toxins.

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Mathematics Subject Classification: Primary: 34C25, 34D05, 92D25; Secondary: 34D20, 37C25.

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References

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