Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model
In this paper, we present new results on deterministic sudden changes and stochastic fluctuations’ effects on the dynamics of a two-predator one-prey model. We purpose to study the dynamics of the model with some impacting factors as the problem statement. The methodology depends on investigating th...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6611970 |
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| author | Jawdat Alebraheem Nasser S. Elazab Mogtaba Mohammed Anis Riahi Ahmed Elmoasry |
| author_facet | Jawdat Alebraheem Nasser S. Elazab Mogtaba Mohammed Anis Riahi Ahmed Elmoasry |
| author_sort | Jawdat Alebraheem |
| collection | DOAJ |
| description | In this paper, we present new results on deterministic sudden changes and stochastic fluctuations’ effects on the dynamics of a two-predator one-prey model. We purpose to study the dynamics of the model with some impacting factors as the problem statement. The methodology depends on investigating the seasonality and stochastic terms which make the predator-prey interactions more realistic. A theoretical analysis is introduced for studying the effects of sudden deterministic changes, using three different cases of sudden changes. We show that the system in a good situation presents persistence dynamics only as a stable dynamical behavior. However, the system in a bad situation leads to three main outcomes as follows: first, constancy at the initial conditions of the prey and predators; second, extinction of the whole system; third, extinction of both predators, resulting in the growth of the prey population until it reaches a peak carrying capacity. We perform numerical simulations to study effects of stochastic fluctuations, which show that noise strength leads to an increase in the oscillations in the dynamical behavior and became more complex and finally leads to extinction when the strength of the noise is high. The random noises transfer the dynamical behavior from the equilibrium case to the oscillation case, which describes some unstable environments. |
| format | Article |
| id | doaj-art-f754b0a138bb4e8191731fbccc567506 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f754b0a138bb4e8191731fbccc5675062025-02-03T01:28:26ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66119706611970Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey ModelJawdat Alebraheem0Nasser S. Elazab1Mogtaba Mohammed2Anis Riahi3Ahmed Elmoasry4Department of Mathematics, College of Science Al Zufli, Majmaah University, Majmaah 11952, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Cairo University, Giza, EgyptDepartment of Mathematics, College of Science Al Zufli, Majmaah University, Majmaah 11952, Saudi ArabiaDepartment of Mathematics, College of Science Al Zufli, Majmaah University, Majmaah 11952, Saudi ArabiaDepartment of Mathematics, College of Science Al Zufli, Majmaah University, Majmaah 11952, Saudi ArabiaIn this paper, we present new results on deterministic sudden changes and stochastic fluctuations’ effects on the dynamics of a two-predator one-prey model. We purpose to study the dynamics of the model with some impacting factors as the problem statement. The methodology depends on investigating the seasonality and stochastic terms which make the predator-prey interactions more realistic. A theoretical analysis is introduced for studying the effects of sudden deterministic changes, using three different cases of sudden changes. We show that the system in a good situation presents persistence dynamics only as a stable dynamical behavior. However, the system in a bad situation leads to three main outcomes as follows: first, constancy at the initial conditions of the prey and predators; second, extinction of the whole system; third, extinction of both predators, resulting in the growth of the prey population until it reaches a peak carrying capacity. We perform numerical simulations to study effects of stochastic fluctuations, which show that noise strength leads to an increase in the oscillations in the dynamical behavior and became more complex and finally leads to extinction when the strength of the noise is high. The random noises transfer the dynamical behavior from the equilibrium case to the oscillation case, which describes some unstable environments.http://dx.doi.org/10.1155/2021/6611970 |
| spellingShingle | Jawdat Alebraheem Nasser S. Elazab Mogtaba Mohammed Anis Riahi Ahmed Elmoasry Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model Journal of Mathematics |
| title | Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model |
| title_full | Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model |
| title_fullStr | Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model |
| title_full_unstemmed | Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model |
| title_short | Deterministic Sudden Changes and Stochastic Fluctuation Effects on Stability and Persistence Dynamics of Two-Predator One-Prey Model |
| title_sort | deterministic sudden changes and stochastic fluctuation effects on stability and persistence dynamics of two predator one prey model |
| url | http://dx.doi.org/10.1155/2021/6611970 |
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