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Vietnam Journal of Mathematics 39:4 (2011) 465-483

Extinction of Species in Discrete Models of Lotka-Volterra Type

with Infinite Delay

Trinh Tuan Anh¹ and Pham Minh Thong²

¹Faculty of Mathematics and Informatics, Hanoi National University of Education,

Hanoi, Vietnam

²Faculty of Mathematics and Informatics, Tay Bac University, Son La, Vietnam

Abstract. A discrete model of nonautonomous competitive Lotka-Volterra type with infinite delay for d species is considered. It is shown that if coefficients satisfy some certain inequalities, then any solution with positive components at some point will have all of its last d-1 components tending to zero, while the first one will approach to a positive solution of a logistic equation.

2000 Mathematics Subject Classification: 34A12, 39A10, 34C11, 34C27, 92B05.

Keywords: Extinction, discrete model of Lotka-Volterra type, logistic equation.

Established by Vietnam Academy of Science and Technology & Vietnam Mathematical Society

Published by Springer since January 2013