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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.

 

 

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