Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses
Joint Authors
Luo, Zhenguo
Luo, Liping
Huang, Jianhua
Dai, Binxiang
Source
International Journal of Differential Equations
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-26
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
We consider the following generalized n-species Lotka-Volterra type and Gilpin-Ayala type competition systems with multiple delays and impulses: xi′(t)=xi(t)[ai(t)-bi(t)xi(t)-∑j=1ncij(t)xjαij(t-ρij(t))-∑j=1ndij(t)xjβij(t-τij(t))-∑j=1neij(t)∫-ηij0kij(s)xjγij(t+s)ds-∑j=1nfij(t)∫-θij0Kij(ξ)xiδij(t+ξ)xjσij(t+ξ)dξ],a.e, t>0, t≠tk; xi(tk+)-xi(tk-)=hikxi(tk), i=1,2,…,n, k∈Z+.
By applying the Krasnoselskii fixed-point theorem in a cone of Banach space, we derive some verifiable necessary and sufficient conditions for the existence of positive periodic solutions of the previously mentioned.
As applications, some special cases of the previous system are examined and some earlier results are extended and improved.
American Psychological Association (APA)
Luo, Zhenguo& Luo, Liping& Huang, Jianhua& Dai, Binxiang. 2013. Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses. International Journal of Differential Equations،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-485529
Modern Language Association (MLA)
Luo, Zhenguo…[et al.]. Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses. International Journal of Differential Equations No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-485529
American Medical Association (AMA)
Luo, Zhenguo& Luo, Liping& Huang, Jianhua& Dai, Binxiang. Global Positive Periodic Solutions of Generalized n-Species Gilpin-Ayala Delayed Competition Systems with Impulses. International Journal of Differential Equations. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-485529
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-485529