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标题：New conditions on the existence and stability of positive periodic solutions for n -species Lotka-Volterra systems with deviating arguments
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作者：Yan Xu ; Zhimin He
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2014
卷号：2014
期号：1
页码：93
DOI：10.1186/1687-1847-2014-93
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the existence and stability of positive periodic solutions for an n-species Lotka-Volterra system with deviating arguments, x i ′ ( t ) = x i ( t ) ( b i r i ( t ) − a i i ( t ) x i ( t − τ i i ( t ) ) − ∑ j = 1 , j ≠ i n k i j a i j ( t ) x j ( t − τ i j ( t ) ) ) , i = 1 , 2 , … , n , referred to as (E). By using Mawhin’s coincidence degree, matrix spectral theory, and some new estimation techniques for the prior bounds of unknown solutions to the equation L x = λ N x , some new and interesting sufficient conditions are obtained guaranteeing the existence and global stability of positive periodic solutions of the above system. The model studied in this paper is more general, and it includes some known Lotka-Volterra type systems, such as competitive systems, predator-prey systems, and competitor-mutualist systems. Our new results are different from the known results in the previous literature. MSC:34K13, 37B25.
关键词：positive periodic solutions ; Lotka-Volterra systems ; coincidence degree ; global asymptotic stability