Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey
In this article, the use of predator-dependent functional and numerical responses is proposed to form an autonomous predator–prey model. The dynamic behaviors of this model were analytically studied. The boundedness of the proposed model was proven; then, the Kolmogorov analysis was used for validat...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-01-01
|
| Series: | Diversity |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1424-2818/13/1/23 |
| _version_ | 1797413589531754496 |
|---|---|
| author | Jawdat Alebraheem |
| author_facet | Jawdat Alebraheem |
| author_sort | Jawdat Alebraheem |
| collection | DOAJ |
| description | In this article, the use of predator-dependent functional and numerical responses is proposed to form an autonomous predator–prey model. The dynamic behaviors of this model were analytically studied. The boundedness of the proposed model was proven; then, the Kolmogorov analysis was used for validating and identifying the coexistence and extinction conditions of the model. In addition, the local and global stability conditions of the model were determined. Moreover, a novel idea was introduced by adding the oscillation of the immigration of the prey into the model which forms a non-autonomous model. The numerically obtained results display that the dynamic behaviors of the model exhibit increasingly stable fluctuations and an increased likelihood of coexistence compared to the autonomous model. |
| first_indexed | 2024-03-09T05:20:09Z |
| format | Article |
| id | doaj.art-69f21754ac974ac793480fe2cccfce23 |
| institution | Directory Open Access Journal |
| issn | 1424-2818 |
| language | English |
| last_indexed | 2024-03-09T05:20:09Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Diversity |
| spelling | doaj.art-69f21754ac974ac793480fe2cccfce232023-12-03T12:41:05ZengMDPI AGDiversity1424-28182021-01-011312310.3390/d13010023Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the PreyJawdat Alebraheem0Department of Mathematics, College of Science Al Zufli, Majmaah University, Majmaah 11952, Saudi ArabiaIn this article, the use of predator-dependent functional and numerical responses is proposed to form an autonomous predator–prey model. The dynamic behaviors of this model were analytically studied. The boundedness of the proposed model was proven; then, the Kolmogorov analysis was used for validating and identifying the coexistence and extinction conditions of the model. In addition, the local and global stability conditions of the model were determined. Moreover, a novel idea was introduced by adding the oscillation of the immigration of the prey into the model which forms a non-autonomous model. The numerically obtained results display that the dynamic behaviors of the model exhibit increasingly stable fluctuations and an increased likelihood of coexistence compared to the autonomous model.https://www.mdpi.com/1424-2818/13/1/23stability analysiscoexistenceimmigrationoscillationKolmogorov analysispredator–prey model |
| spellingShingle | Jawdat Alebraheem Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey Diversity stability analysis coexistence immigration oscillation Kolmogorov analysis predator–prey model |
| title | Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey |
| title_full | Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey |
| title_fullStr | Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey |
| title_full_unstemmed | Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey |
| title_short | Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey |
| title_sort | dynamics of a predator prey model with the effect of oscillation of immigration of the prey |
| topic | stability analysis coexistence immigration oscillation Kolmogorov analysis predator–prey model |
| url | https://www.mdpi.com/1424-2818/13/1/23 |
| work_keys_str_mv | AT jawdatalebraheem dynamicsofapredatorpreymodelwiththeeffectofoscillationofimmigrationoftheprey |