Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales
We investigate a nonautonomous ratio-dependent predator-prey model with Beddington-DeAngelis functional response and multiple harvesting (or exploited) terms on time scales. By means of using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence o...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/243974 |
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| _version_ | 1850174330454933504 |
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| author | Zhenjie Liu |
| author_facet | Zhenjie Liu |
| author_sort | Zhenjie Liu |
| collection | DOAJ |
| description | We investigate a nonautonomous ratio-dependent predator-prey model with Beddington-DeAngelis functional response and multiple harvesting (or exploited) terms on time scales. By means of using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of at least two periodic solutions for the system. Moreover, when the time scale 𝕋 is chosen as ℝ or ℤ, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. |
| format | Article |
| id | doaj-art-d66f18e5dd9144ffbc7938ce30b19554 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d66f18e5dd9144ffbc7938ce30b195542025-08-20T02:19:40ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/243974243974Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time ScalesZhenjie Liu0School of Mathematics and Computer, Harbin University, Harbin, Heilongjiang 150086, ChinaWe investigate a nonautonomous ratio-dependent predator-prey model with Beddington-DeAngelis functional response and multiple harvesting (or exploited) terms on time scales. By means of using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of at least two periodic solutions for the system. Moreover, when the time scale 𝕋 is chosen as ℝ or ℤ, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.http://dx.doi.org/10.1155/2009/243974 |
| spellingShingle | Zhenjie Liu Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales Discrete Dynamics in Nature and Society |
| title | Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales |
| title_full | Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales |
| title_fullStr | Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales |
| title_full_unstemmed | Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales |
| title_short | Double Periodic Solutions for a Ratio-Dependent Predator-Prey System with Harvesting Terms on Time Scales |
| title_sort | double periodic solutions for a ratio dependent predator prey system with harvesting terms on time scales |
| url | http://dx.doi.org/10.1155/2009/243974 |
| work_keys_str_mv | AT zhenjieliu doubleperiodicsolutionsforaratiodependentpredatorpreysystemwithharvestingtermsontimescales |