Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays
We consider a predator-prey system with Beddington-DeAngelis functional response and delays, in which not only the stage structure on prey but also the delay due to digestion is considered. First, we give a sufficient and necessary condition for the existence of a unique positive equilibrium by anal...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/930762 |
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| _version_ | 1832549467910307840 |
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| author | Nai-Wei Liu Ting-Ting Kong |
| author_facet | Nai-Wei Liu Ting-Ting Kong |
| author_sort | Nai-Wei Liu |
| collection | DOAJ |
| description | We consider a predator-prey system with Beddington-DeAngelis functional
response and delays, in which not only the stage structure on prey but also the
delay due to digestion is considered. First, we give a sufficient and necessary condition
for the existence of a unique positive equilibrium by analyzing the corresponding
locations of a hyperbolic curve and a line. Then, by constructing an appropriate Lyapunov
function, we prove that the positive equilibrium is locally asymptotically stable
under a sufficient condition. Finally, by using comparison theorem and the ω-limit set
theory, we study the global asymptotic stability of the boundary equilibrium and the
positive equilibrium, respectively. Also, we obtain a sufficient condition to assure the
global asymptotic stability. |
| format | Article |
| id | doaj-art-bd9f5f49c42847929de245dc4b1a9043 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-bd9f5f49c42847929de245dc4b1a90432025-02-03T06:11:20ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/930762930762Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and DelaysNai-Wei Liu0Ting-Ting Kong1School of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, ChinaSchool of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, ChinaWe consider a predator-prey system with Beddington-DeAngelis functional response and delays, in which not only the stage structure on prey but also the delay due to digestion is considered. First, we give a sufficient and necessary condition for the existence of a unique positive equilibrium by analyzing the corresponding locations of a hyperbolic curve and a line. Then, by constructing an appropriate Lyapunov function, we prove that the positive equilibrium is locally asymptotically stable under a sufficient condition. Finally, by using comparison theorem and the ω-limit set theory, we study the global asymptotic stability of the boundary equilibrium and the positive equilibrium, respectively. Also, we obtain a sufficient condition to assure the global asymptotic stability.http://dx.doi.org/10.1155/2014/930762 |
| spellingShingle | Nai-Wei Liu Ting-Ting Kong Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays Abstract and Applied Analysis |
| title | Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays |
| title_full | Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays |
| title_fullStr | Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays |
| title_full_unstemmed | Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays |
| title_short | Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays |
| title_sort | dynamics of a predator prey system with beddington deangelis functional response and delays |
| url | http://dx.doi.org/10.1155/2014/930762 |
| work_keys_str_mv | AT naiweiliu dynamicsofapredatorpreysystemwithbeddingtondeangelisfunctionalresponseanddelays AT tingtingkong dynamicsofapredatorpreysystemwithbeddingtondeangelisfunctionalresponseanddelays |