Multiple Periodicity in a Predator–Prey Model with Prey Refuge
We consider a delayed prey–predator model incorporating a refuge with a non-monotone functional response. It is supposed that prey can live in the predatory region and prey refuge, respectively. Based on Mawhin’s coincidence degree and nontrivial estimation techniques for a priori bounds of unknown...
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| Format: | Article |
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MDPI AG
2022-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/421 |
| _version_ | 1827660023498539008 |
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| author | Weijie Lu Yonghui Xia |
| author_facet | Weijie Lu Yonghui Xia |
| author_sort | Weijie Lu |
| collection | DOAJ |
| description | We consider a delayed prey–predator model incorporating a refuge with a non-monotone functional response. It is supposed that prey can live in the predatory region and prey refuge, respectively. Based on Mawhin’s coincidence degree and nontrivial estimation techniques for a priori bounds of unknown solutions to the operator equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>v</mi><mo>=</mo><mi>λ</mi><mi>N</mi><mi>v</mi></mrow></semantics></math></inline-formula>, we prove the existence of multiple periodic solutions. Finally, an example demonstrates the feasibility of our main results. |
| first_indexed | 2024-03-09T23:32:23Z |
| format | Article |
| id | doaj.art-aca03a2d1a3f4a468a4290804b2c8968 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:32:23Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-aca03a2d1a3f4a468a4290804b2c89682023-11-23T17:07:14ZengMDPI AGMathematics2227-73902022-01-0110342110.3390/math10030421Multiple Periodicity in a Predator–Prey Model with Prey RefugeWeijie Lu0Yonghui Xia1Department of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaWe consider a delayed prey–predator model incorporating a refuge with a non-monotone functional response. It is supposed that prey can live in the predatory region and prey refuge, respectively. Based on Mawhin’s coincidence degree and nontrivial estimation techniques for a priori bounds of unknown solutions to the operator equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>v</mi><mo>=</mo><mi>λ</mi><mi>N</mi><mi>v</mi></mrow></semantics></math></inline-formula>, we prove the existence of multiple periodic solutions. Finally, an example demonstrates the feasibility of our main results.https://www.mdpi.com/2227-7390/10/3/421periodic solutionsprey refugenon-monotone functional response |
| spellingShingle | Weijie Lu Yonghui Xia Multiple Periodicity in a Predator–Prey Model with Prey Refuge Mathematics periodic solutions prey refuge non-monotone functional response |
| title | Multiple Periodicity in a Predator–Prey Model with Prey Refuge |
| title_full | Multiple Periodicity in a Predator–Prey Model with Prey Refuge |
| title_fullStr | Multiple Periodicity in a Predator–Prey Model with Prey Refuge |
| title_full_unstemmed | Multiple Periodicity in a Predator–Prey Model with Prey Refuge |
| title_short | Multiple Periodicity in a Predator–Prey Model with Prey Refuge |
| title_sort | multiple periodicity in a predator prey model with prey refuge |
| topic | periodic solutions prey refuge non-monotone functional response |
| url | https://www.mdpi.com/2227-7390/10/3/421 |
| work_keys_str_mv | AT weijielu multipleperiodicityinapredatorpreymodelwithpreyrefuge AT yonghuixia multipleperiodicityinapredatorpreymodelwithpreyrefuge |