Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay
In this paper, a prey-predator model and weak Allee effect in prey growth and its dynamical behaviors are studied in detail. The existence, boundedness, and stability of the equilibria of the model are qualitatively discussed. Bifurcation analysis is also taken into account. After incorporating the...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/7296461 |
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| _version_ | 1832567780918951936 |
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| author | Yong Ye Hua Liu Yu-mei Wei Ming Ma Kai Zhang |
| author_facet | Yong Ye Hua Liu Yu-mei Wei Ming Ma Kai Zhang |
| author_sort | Yong Ye |
| collection | DOAJ |
| description | In this paper, a prey-predator model and weak Allee effect in prey growth and its dynamical behaviors are studied in detail. The existence, boundedness, and stability of the equilibria of the model are qualitatively discussed. Bifurcation analysis is also taken into account. After incorporating the searching delay and digestion delay, we establish a delayed predator-prey system with Allee effect. The results show that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values. Finally, we present some numerical simulations to illustrate our theoretical analysis. |
| format | Article |
| id | doaj-art-231eff366eae46388d239fa5a40fd4fc |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-231eff366eae46388d239fa5a40fd4fc2025-02-03T01:00:31ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/72964617296461Dynamic Study of a Predator-Prey Model with Weak Allee Effect and DelayYong Ye0Hua Liu1Yu-mei Wei2Ming Ma3Kai Zhang4School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaExperimental Center, Northwest Minzu University, Lanzhou 730000, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaSchool of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, ChinaIn this paper, a prey-predator model and weak Allee effect in prey growth and its dynamical behaviors are studied in detail. The existence, boundedness, and stability of the equilibria of the model are qualitatively discussed. Bifurcation analysis is also taken into account. After incorporating the searching delay and digestion delay, we establish a delayed predator-prey system with Allee effect. The results show that there exist stability switches and Hopf bifurcation occurs while the delay crosses a set of critical values. Finally, we present some numerical simulations to illustrate our theoretical analysis.http://dx.doi.org/10.1155/2019/7296461 |
| spellingShingle | Yong Ye Hua Liu Yu-mei Wei Ming Ma Kai Zhang Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay Advances in Mathematical Physics |
| title | Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay |
| title_full | Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay |
| title_fullStr | Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay |
| title_full_unstemmed | Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay |
| title_short | Dynamic Study of a Predator-Prey Model with Weak Allee Effect and Delay |
| title_sort | dynamic study of a predator prey model with weak allee effect and delay |
| url | http://dx.doi.org/10.1155/2019/7296461 |
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