Global Positive Periodic Solutions of Generalized n‐Species Competition Systems with Multiple Delays and Impulses

Zhenguo Luo and Liping Luo

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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)∫-σij0 fij(s)xj(t+s)ds], a.e., t>0,t≠tk, k∈Z+, i=1,21,21,21,2,…,n; xi(tk+)-xi(tk-)=θikxi(tk), i=,…,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)∫-σij0 fij(s)xj(t+s)ds], a.e., t>0, t≠tk, k∈Z+, i=,…,n; xi(tk+)-xi(tk-)=θikxi(tk), i=,…,n, k∈Z+. It improves and generalizes a series of the well‐known sufficiency theorems in the literature about the problems mentioned previously.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/980974

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:980974

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().