Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species
Our study focuses on analyzing the behavior of a stochastic predator–prey model with a time delay and logistic growth of prey, influenced by Lévy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive solution that spans globally. Subsequently, we explore the conditi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/7/1595 |
| _version_ | 1827746733252149248 |
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| author | Jaouad Danane Delfim F. M. Torres |
| author_facet | Jaouad Danane Delfim F. M. Torres |
| author_sort | Jaouad Danane |
| collection | DOAJ |
| description | Our study focuses on analyzing the behavior of a stochastic predator–prey model with a time delay and logistic growth of prey, influenced by Lévy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive solution that spans globally. Subsequently, we explore the conditions under which extinction occurs, and identify adequate criteria for persistence. Finally, we validate our theoretical findings through numerical simulations, which also helps illustrate the dynamics of the stochastic delayed predator–prey model based on different criteria. |
| first_indexed | 2024-03-11T05:30:28Z |
| format | Article |
| id | doaj.art-35dd9a586e994737b731f198dd34e1c7 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T05:30:28Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-35dd9a586e994737b731f198dd34e1c72023-11-17T17:07:52ZengMDPI AGMathematics2227-73902023-03-01117159510.3390/math11071595Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey SpeciesJaouad Danane0Delfim F. M. Torres1Laboratory of Systems, Modelization and Analysis for Decision Support, National School of Applied Sciences (ENSA), University Hassan 1st of Settat, Berrechid B.P 218, MoroccoCenter for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, PortugalOur study focuses on analyzing the behavior of a stochastic predator–prey model with a time delay and logistic growth of prey, influenced by Lévy noise. Initially, we establish the existence, uniqueness, and boundedness of a positive solution that spans globally. Subsequently, we explore the conditions under which extinction occurs, and identify adequate criteria for persistence. Finally, we validate our theoretical findings through numerical simulations, which also helps illustrate the dynamics of the stochastic delayed predator–prey model based on different criteria.https://www.mdpi.com/2227-7390/11/7/1595prey–predator systemstochastic persistence and extinctionlogistic growth rateLévy noisetime delays |
| spellingShingle | Jaouad Danane Delfim F. M. Torres Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species Mathematics prey–predator system stochastic persistence and extinction logistic growth rate Lévy noise time delays |
| title | Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species |
| title_full | Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species |
| title_fullStr | Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species |
| title_full_unstemmed | Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species |
| title_short | Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species |
| title_sort | three species predator prey stochastic delayed model driven by levy jumps and with cooperation among prey species |
| topic | prey–predator system stochastic persistence and extinction logistic growth rate Lévy noise time delays |
| url | https://www.mdpi.com/2227-7390/11/7/1595 |
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