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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/940287 |
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| _version_ | 1850175808270761984 |
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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. |
| format | Article |
| id | doaj-art-c091e950c8274c4cb78c44ec57e69159 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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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