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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.54 no.1 Bogotá Jan./June 2020
https://doi.org/10.15446/recolma.v54n1.89791
Original articles
Extinction and survival in competitive Lotka-Volterra systems with constant coefficients and infinite delays
Extinción y sobrevivencia en sistemas competitivos de Lotka-Volterra con coeficientes constantes y retardos infinitos
1 Universidad Centro Occidental Lisandro Alvarado, Barquisimeto, Estado Lara, Venezuela
2 Escuela Superior Politécnica del Litoral, ESPOL, FCNM, Guayaquil, Ecuador
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
Se estudian las propiedades cualitativas de un sistema competitivo no autónomo de Lotka-Volterra con retardo infinito.
Mediante el uso de un resultado de la teoría de matrices y del lema de fluctuaciones, se establecen una serie de condiciones algebraicas, fácilmente verificables, sobre los coeficientes y los núcleos, que son suficientes para garantizar la extinción y la sobrevivencia de un determinado número de especies. La parte sobreviviente se estabiliza alrededor de un punto de equilibrio globalmente estable de un subsistema del sistema en estudio. Estas condiciones también garantizan el comportamiento asintótico del sistema.
Palabras clave: Sistemas de Lotka-Volterra; extinción; sobrevivencia; estabilidad; retardo; persistencia
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Received: October 06, 2019; Accepted: May 27, 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
