Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects
We investigate the existence of periodic solutions for a predator-prey system with Holling function response and mutual interference. Our model is more general than others since it has both Holling type IV function and impulsive effects. With some new analytical tricks and the continuation theorem i...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/138984 |
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| _version_ | 1832550069246623744 |
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| author | Haidong Liu Fanwei Meng |
| author_facet | Haidong Liu Fanwei Meng |
| author_sort | Haidong Liu |
| collection | DOAJ |
| description | We investigate the existence of periodic solutions for a predator-prey system with Holling function response and mutual interference. Our model is more general than others since it has both Holling type IV function and impulsive effects. With some new analytical tricks and the continuation theorem in coincidence degree theory proposed by Gaines and Mawhin, we obtain a set of sufficient conditions on the existence of positive periodic solutions for such a system. In addition, in the remark, we point out some minor errors which appeared in the proof of theorems in some published papers with relevant predator-prey models. An example is given to illustrate our results. |
| format | Article |
| id | doaj-art-6195814ca5e44549b4b54f00e04bb991 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-6195814ca5e44549b4b54f00e04bb9912025-02-03T06:07:49ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/138984138984Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive EffectsHaidong Liu0Fanwei Meng1School of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaSchool of Mathematical Sciences, Qufu Normal University, Qufu 273165, ChinaWe investigate the existence of periodic solutions for a predator-prey system with Holling function response and mutual interference. Our model is more general than others since it has both Holling type IV function and impulsive effects. With some new analytical tricks and the continuation theorem in coincidence degree theory proposed by Gaines and Mawhin, we obtain a set of sufficient conditions on the existence of positive periodic solutions for such a system. In addition, in the remark, we point out some minor errors which appeared in the proof of theorems in some published papers with relevant predator-prey models. An example is given to illustrate our results.http://dx.doi.org/10.1155/2015/138984 |
| spellingShingle | Haidong Liu Fanwei Meng Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects Discrete Dynamics in Nature and Society |
| title | Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects |
| title_full | Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects |
| title_fullStr | Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects |
| title_full_unstemmed | Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects |
| title_short | Existence of Positive Periodic Solutions for a Predator-Prey System of Holling Type IV Function Response with Mutual Interference and Impulsive Effects |
| title_sort | existence of positive periodic solutions for a predator prey system of holling type iv function response with mutual interference and impulsive effects |
| url | http://dx.doi.org/10.1155/2015/138984 |
| work_keys_str_mv | AT haidongliu existenceofpositiveperiodicsolutionsforapredatorpreysystemofhollingtypeivfunctionresponsewithmutualinterferenceandimpulsiveeffects AT fanweimeng existenceofpositiveperiodicsolutionsforapredatorpreysystemofhollingtypeivfunctionresponsewithmutualinterferenceandimpulsiveeffects |