Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales
This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predator-prey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic sol...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/928704 |
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| _version_ | 1832549412696489984 |
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| author | Xiaoquan Ding Gaifang Zhao |
| author_facet | Xiaoquan Ding Gaifang Zhao |
| author_sort | Xiaoquan Ding |
| collection | DOAJ |
| description | This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predator-prey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin, and the Smith growth, and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod-Haldane type, and the Beddington-DeAngelis type, the system always has at least one periodic solution. Some known results are shown to be special cases of the present paper. |
| format | Article |
| id | doaj-art-f1c4c32b886d48b5bec1b1700a38041c |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f1c4c32b886d48b5bec1b1700a38041c2025-02-03T06:11:24ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/928704928704Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time ScalesXiaoquan Ding0Gaifang Zhao1School of Mathematics and Statistics, Henan University of Science and Technology, Henan, Luoyang 471003, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Henan, Luoyang 471003, ChinaThis paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predator-prey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin, and the Smith growth, and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod-Haldane type, and the Beddington-DeAngelis type, the system always has at least one periodic solution. Some known results are shown to be special cases of the present paper.http://dx.doi.org/10.1155/2012/928704 |
| spellingShingle | Xiaoquan Ding Gaifang Zhao Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales Discrete Dynamics in Nature and Society |
| title | Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales |
| title_full | Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales |
| title_fullStr | Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales |
| title_full_unstemmed | Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales |
| title_short | Periodic Solutions for a Semi-Ratio-Dependent Predator-Prey System with Delays on Time Scales |
| title_sort | periodic solutions for a semi ratio dependent predator prey system with delays on time scales |
| url | http://dx.doi.org/10.1155/2012/928704 |
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