Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance
Abstract
:1. Introduction
2. Preliminaries
3. Extinction and Persistence in Mean
4. Stationary Distribution
5. Numerical Simulations
6. Conclusions
- (1)
- If holds, the predator can be extinct.
- (2)
- When holds, the prey can be persistent and have a unique ergodic stationary distribution.
- (3)
- When , the predator can be persistent in the mean.
- (4)
- When , then model has a unique ergodic stationary distribution.
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | Biological Significance |
---|---|
The birth rate of prey. | |
The natural death rate of prey. | |
d | The natural death rate of predator. |
The attack rate per predator to prey. | |
The predator’s handing time of prey. | |
k | Conversion efficiency. |
Parameter of predator in hunting cooperation. |
Parameter Values | Case 1 | Case 2 |
---|---|---|
0.5 | 0.5 | |
0.24 | 0.8 | |
0.6 | 0.6 | |
0.24 | 0.24 | |
d | 0.2 | 0.2 |
1.2 | 1.2 | |
k | 0.7 | 0.7 |
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Zhang, Y.; Meng, X. Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance. Mathematics 2022, 10, 2890. https://doi.org/10.3390/math10162890
Zhang Y, Meng X. Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance. Mathematics. 2022; 10(16):2890. https://doi.org/10.3390/math10162890
Chicago/Turabian StyleZhang, Yuke, and Xinzhu Meng. 2022. "Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance" Mathematics 10, no. 16: 2890. https://doi.org/10.3390/math10162890
APA StyleZhang, Y., & Meng, X. (2022). Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance. Mathematics, 10(16), 2890. https://doi.org/10.3390/math10162890