|
|
具有合作捕食与种内竞争的一类捕食者–食饵模型的Hopf分支
|
Abstract:
本文研究了一类具有合作捕食和种内竞争的捕食者–食饵模型。该模型的参数空间被划分为几个不同的区域，在每个参数区域，研究了系统的动力学行为，包括内平衡点的个数、稳定性和Hopf分支。结果表明该模型会发生两次Hopf分支。分别与没有合作捕食和不存在种内竞争的捕食者–食饵模型进行比较，指出Hopf分支的发生是由合作捕食引起的，而两次Hopf分支是由种内竞争引起的。
We consider a predator-prey model with cooperative hunting and intraspecific competition in predators. The parameter space of the model is divided into several mutually exclusive regions. In each region, the dynamics of the system is investigated, including the number of interior equilibria, stability and Hopf bifurcation. It is presented that Hopf bifurcation may occur twice. By comparing to the dynamics of the systems without cooperative hunting and without the intraspecific competi-tion in predators, respectively, it is shown that the occurrence of Hopf bifurcation is caused by in-traspecific competition.
| [1] | Packer, C. and Ruttan, L. (1988) The Evolution of Cooperative Hunting. The American Naturalist, 132, 159-198.
https://doi.org/10.1086/284844 |
| [2] | Macdonald, D.W. (1983) The Ecology of Carnivore Social Behaviour. Nature, 301, 379-384.
https://doi.org/10.1038/301379a0 |
| [3] | Cosner, C., DeAngelis, D.L., Ault, J.S. and Olson, D.B. (1999) Effects of Spatial Grouping on the Functional Response of Predators. Theoretical Population Biology, 56, 65-75. https://doi.org/10.1006/tpbi.1999.1414 |
| [4] | Berec, L. (2010) Impacts of Foraging Facilitation among Predators on Predator-Prey Dynamics. Bulletin of Mathematical Biology, 72, 94-121. https://doi.org/10.1007/s11538-009-9439-1 |
| [5] | Pal, S., Pal, N., Samanta, S. and Chattopadhyay, J. (2019) Fear Effect in Prey and Hunting Cooperation among Predators in a Leslie-Gower Model. Mathematical Biosciences and En-gineering, 16, 5146-5179.
https://doi.org/10.3934/mbe.2019258 |
| [6] | Duarte, J., Januário, C., Martins, N. and Sardanyés, J. (2009) Chaos and Crises in a Model for Cooperative Hunting: A Symbolic Dynamics Approach. Chaos, 19, Article ID: 043102. https://doi.org/10.1063/1.3243924 |
| [7] | Fu, S. and Zhang, H. (2021) Effect of Hunting Cooperation on the Dynam-ic Behavior for a Diffusive Holling Type II Predator-Prey Model. Communications in Nonlinear Science and Numerical Simulation, 99, Article ID: 105807.
https://doi.org/10.1016/j.cnsns.2021.105807 |
| [8] | Song, D., Li, C. and Song, Y. (2020) Stability and Cross-Diffusion-Driven Instability in a Diffusive Predator-Prey System with Hunting Cooperation Functional Response. Nonlinear Analysis: Real World Applications, 54, Article ID: 103106. https://doi.org/10.1016/j.nonrwa.2020.103106 |
| [9] | Vishwakarma, K. and Sen, M. (2021) Role of Allee Effect in Prey and Hunting Cooperation in a Generalist Predator. Mathematics and Computers in Simulation, 190, 622-640. https://doi.org/10.1016/j.matcom.2021.05.023 |
| [10] | Vishwakarma, K. and Sen, M. (2022) Influence of Allee Effect in Prey and Hunting Cooperation in Predator with Holling Type-III Functional Response. Journal of Applied Mathemat-ics and Computing, 68, 249-269.
https://doi.org/10.1007/s12190-021-01520-1 |
| [11] | Wu, D. and Zhao, M. (2019) Qualitative Analysis for a Diffusive Predator-Prey Model with Hunting Cooperative. Physica A, 515, 299-309. https://doi.org/10.1016/j.physa.2018.09.176 |
| [12] | Zhang, J. and Zhang, W. (2020) Dynamics of a Predator-Prey Model with Hunting Cooperation and Allee Effects in Predators. International Journal of Bifurcation and Chaos, 30, Ar-ticle ID: 2050199.
https://doi.org/10.1142/S0218127420501990 |
| [13] | Alves, M.T. and Hilker, F.M. (2017) Hunting Cooperation and Allee Effects in Predators. Journal of Theoretical Biology, 419, 13-22. https://doi.org/10.1016/j.jtbi.2017.02.002 |
| [14] | Dumortir, F., Llibre, J. and Artés, J.C. (2006) Qualitative Theory of Planar Differential Systems. Springer, Berlin. |
| [15] | Wiggins, S. (1990) Introduction to Applied Nonlinear Dynamical Systems and Chaos. Texts in Applied Mathematics. 2nd Edition, Springer, Berlin. https://doi.org/10.1007/978-1-4757-4067-7 |
| [16] | Guckenheimer, J. and Holmes, P. (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, Berlin. https://doi.org/10.1007/978-1-4612-1140-2 |
