Abstract

MONTES DE OCA, Francisco  and  PEREZ, Liliana Rebeca. Extinction and survival in competitive Lotka-Volterra systems with constant coefficients and infinite delays. Rev.colomb.mat. [online]. 2020, vol.54, n.1, pp.75-91. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v54n1.89791.

The qualitative properties of a nonautonomous competitive Lotka-Volterra system with infinite delays are studied.

By using a result of matrix theory and the fluctuation lemma, we establish a series of easily verifiable algebraic conditions on the coefficients and the kernel, which are sufficient to ensure the survival and the extinction of a determined number of species. The surviving part is stabilized around a globally stable critical point of a subsystem of the system under study. These conditions also guarantee the asymptotic behavior of the system.

Keywords : Lotka-Volterra system; extinction; competition; stability; delay; persistence.

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