Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System

This paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model with M-predators and N-preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability...

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Main Authors: Yong-Hui Xia, Xiang Gu, Patricia J. Y. Wong, Syed Abbas
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/940287
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author Yong-Hui Xia
Xiang Gu
Patricia J. Y. Wong
Syed Abbas
author_facet Yong-Hui Xia
Xiang Gu
Patricia J. Y. Wong
Syed Abbas
author_sort Yong-Hui Xia
collection DOAJ
description This paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model with M-predators and N-preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability of the periodic solution. The existence and stability conditions are given in terms of spectral radius of explicit matrices which are much different from the conditions given by the algebraic inequalities. Finally, an example is given to show the feasibility of our results.
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publishDate 2012-01-01
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spelling doaj-art-c091e950c8274c4cb78c44ec57e691592025-08-20T02:19:22ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/940287940287Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed SystemYong-Hui Xia0Xiang Gu1Patricia J. Y. Wong2Syed Abbas3Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaSchool of Electrical and Electronic Engineering, Nanyang Technological University, 639798, SingaporeSchool of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175001, IndiaThis paper gives an application of Mawhin’s coincidence degree and matrix spectral theory to a predator-prey model with M-predators and N-preys. The method is different from that used in the previous work. Some new sufficient conditions are obtained for the existence and global asymptotic stability of the periodic solution. The existence and stability conditions are given in terms of spectral radius of explicit matrices which are much different from the conditions given by the algebraic inequalities. Finally, an example is given to show the feasibility of our results.http://dx.doi.org/10.1155/2012/940287
spellingShingle Yong-Hui Xia
Xiang Gu
Patricia J. Y. Wong
Syed Abbas
Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System
Abstract and Applied Analysis
title Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System
title_full Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System
title_fullStr Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System
title_full_unstemmed Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System
title_short Application of Mawhin's Coincidence Degree and Matrix Spectral Theory to a Delayed System
title_sort application of mawhin s coincidence degree and matrix spectral theory to a delayed system
url http://dx.doi.org/10.1155/2012/940287
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AT xianggu applicationofmawhinscoincidencedegreeandmatrixspectraltheorytoadelayedsystem
AT patriciajywong applicationofmawhinscoincidencedegreeandmatrixspectraltheorytoadelayedsystem
AT syedabbas applicationofmawhinscoincidencedegreeandmatrixspectraltheorytoadelayedsystem