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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
DOI:
https://doi.org/10.15446/recolma.v54n1.89791Palabras clave:
Lotka-Volterra system, extinction, competition, stability, delay, persistence (en)Sistemas de Lotka-Volterra, extinción, sobrevivencia, estabilidad, retardo, persistencia (es)
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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.
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.
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Derechos de autor 2020 Revista Colombiana de Matemáticas
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
