Global Positive Periodic Solutions of Generalized n-Species Competition Systems with Multiple Delays and Impulses
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-08-26
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
By applying the fixed point theorem in a cone of Banach space, we obtain an easily verifiable necessary and sufficient condition for the existence of positive periodic solutions of two kinds of generalized n-species competition systems with multiple delays and impulses as follows: xi′(t)=xi(t)[ai(t)-bi(t)xi(t)-∑j=1ncij(t)xi(t-τij(t))-∑j=1ndij(t)xj(t-γij(t))-∑j=1neij(t)∫-σij0fij(s)xj(t+s)ds], a.e., t>0,t≠tk, k∈Z+, i=1,2,…,n; xi(tk+)-xi(tk-)=θikxi(tk), i=1,2,…,n, k∈Z+; and xi′(t)=xi(t)[ai(t)-bi(t)xi(t)+∑j=1ncij(t)xi(t-τij(t))-∑j=1ndij(t)xj(t-γij(t))-∑j=1neij(t)∫-σij0fij(s)xj(t+s)ds], a.e., t>0, t≠tk, k∈Z+, i=1,2,…,n; xi(tk+)-xi(tk-)=θikxi(tk), i=1,2,…,n, k∈Z+.
It improves and generalizes a series of the well-known sufficiency theorems in the literature about the problems mentioned previously.
American Psychological Association (APA)
Luo, Zhenguo& Luo, Liping. 2013. Global Positive Periodic Solutions of Generalized n-Species Competition Systems with Multiple Delays and Impulses. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-513260
Modern Language Association (MLA)
Luo, Zhenguo& Luo, Liping. Global Positive Periodic Solutions of Generalized n-Species Competition Systems with Multiple Delays and Impulses. Abstract and Applied Analysis No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-513260
American Medical Association (AMA)
Luo, Zhenguo& Luo, Liping. Global Positive Periodic Solutions of Generalized n-Species Competition Systems with Multiple Delays and Impulses. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-513260
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-513260