# American Institute of Mathematical Sciences

December  2021, 41(12): 5743-5764. doi: 10.3934/dcds.2021094

## 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

Received  March 2021 Revised  May 2021 Published  December 2021 Early access  June 2021

Fund Project: 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)

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.

Citation: Isabel Coelho, Carlota Rebelo, Elisa Sovrano. Extinction or coexistence in periodic Kolmogorov systems of competitive type. Discrete & Continuous Dynamical Systems, 2021, 41 (12) : 5743-5764. doi: 10.3934/dcds.2021094
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