Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay
Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay ̇𝑥1(𝑡)=𝑥1(𝑡)[𝑟1(𝑡)−𝑎11(𝑡)𝑥1(𝑡−𝜏(𝑡))−𝑎12(𝑡)𝑥2(𝑡)/(𝑚2+𝑥21(𝑡))], ̇𝑥2(𝑡)=𝑥2(𝑡)[𝑟2(𝑡)−𝑎21(𝑡)𝑥2(𝑡)/𝑥1(𝑡)], are obtained, where 𝑥1(𝑡) and 𝑥2(𝑡) stand for the density of...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/960823 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553584079667200 |
|---|---|
| author | Xuepeng Li Wensheng Yang |
| author_facet | Xuepeng Li Wensheng Yang |
| author_sort | Xuepeng Li |
| collection | DOAJ |
| description | Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay ̇𝑥1(𝑡)=𝑥1(𝑡)[𝑟1(𝑡)−𝑎11(𝑡)𝑥1(𝑡−𝜏(𝑡))−𝑎12(𝑡)𝑥2(𝑡)/(𝑚2+𝑥21(𝑡))], ̇𝑥2(𝑡)=𝑥2(𝑡)[𝑟2(𝑡)−𝑎21(𝑡)𝑥2(𝑡)/𝑥1(𝑡)], are obtained, where 𝑥1(𝑡) and 𝑥2(𝑡) stand for the density of the prey and the predator, respectively, and 𝑚≠0 is a constant. 𝜏(𝑡)≥0 stands for the time delays due to negative feedback of the prey population. |
| format | Article |
| id | doaj-art-0a68f4d63228460898d5fc993c1e539f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0a68f4d63228460898d5fc993c1e539f2025-02-03T05:53:36ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/960823960823Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time DelayXuepeng Li0Wensheng Yang1School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, ChinaSchool of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, ChinaSufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay ̇𝑥1(𝑡)=𝑥1(𝑡)[𝑟1(𝑡)−𝑎11(𝑡)𝑥1(𝑡−𝜏(𝑡))−𝑎12(𝑡)𝑥2(𝑡)/(𝑚2+𝑥21(𝑡))], ̇𝑥2(𝑡)=𝑥2(𝑡)[𝑟2(𝑡)−𝑎21(𝑡)𝑥2(𝑡)/𝑥1(𝑡)], are obtained, where 𝑥1(𝑡) and 𝑥2(𝑡) stand for the density of the prey and the predator, respectively, and 𝑚≠0 is a constant. 𝜏(𝑡)≥0 stands for the time delays due to negative feedback of the prey population.http://dx.doi.org/10.1155/2009/960823 |
| spellingShingle | Xuepeng Li Wensheng Yang Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay Abstract and Applied Analysis |
| title | Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay |
| title_full | Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay |
| title_fullStr | Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay |
| title_full_unstemmed | Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay |
| title_short | Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay |
| title_sort | permanence of a semi ratio dependent predator prey system with nonmonotonic functional response and time delay |
| url | http://dx.doi.org/10.1155/2009/960823 |
| work_keys_str_mv | AT xuepengli permanenceofasemiratiodependentpredatorpreysystemwithnonmonotonicfunctionalresponseandtimedelay AT wenshengyang permanenceofasemiratiodependentpredatorpreysystemwithnonmonotonicfunctionalresponseandtimedelay |