Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species
Abstract
:1. Introduction
2. Properties of the Solution
2.1. Existence and Uniqueness of a Global Positive Solution
2.2. Stochastic Boundedness
3. Stochastic Extinction of the Prey and Predator
4. Stochastic Extinction of Predator
5. Stochastic Persistence
6. Numerical Simulations
7. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameters | Description |
---|---|
The intrinsic growth rate for prey x | |
The intrinsic growth rate for prey y | |
The carrying capacity for x | |
The carrying capacity for y | |
The predation rate of prey x | |
The predation rate of prey y | |
The rate of cooperation of preys x and y against predator z | |
The predator death rate | |
The rate of intra-species competition within the predators | |
The transformation rate of predator to preys x | |
The transformation rate of predator to preys y |
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Danane, J.; Torres, D.F.M. Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species. Mathematics 2023, 11, 1595. https://doi.org/10.3390/math11071595
Danane J, Torres DFM. Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species. Mathematics. 2023; 11(7):1595. https://doi.org/10.3390/math11071595
Chicago/Turabian StyleDanane, Jaouad, and Delfim F. M. Torres. 2023. "Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species" Mathematics 11, no. 7: 1595. https://doi.org/10.3390/math11071595
APA StyleDanane, J., & Torres, D. F. M. (2023). Three-Species Predator–Prey Stochastic Delayed Model Driven by Lévy Jumps and with Cooperation among Prey Species. Mathematics, 11(7), 1595. https://doi.org/10.3390/math11071595