平方根功能反应捕食者–食饵模型的Hopf分支
Hopf Bifurcation of the Square Root Functional Response Predator-Prey Model
摘要:
本文研究具有避难所的平方根功能反应捕食者–食饵模型的Hopf分支的方向和分支周期解的稳定性。结果表明,当避难所作为参数等于一个阈值时,它会发生Hopf分支。
Abstract:
In this paper, we investigate the direction of Hopf bifurcation and the stability of periodic solution of the bifurcation in a predator-prey model with the square root functional response. The results show that Hopf bifurcation occurs when the refuge as a parameter is equal to a threshold.
参考文献
|
[1]
|
Ajraldi, V., Pittavino, M. and Venturino, E. (2011) Modeling Herd Behavior in Population Systems. Nonlinear Analysis: Real World Applications, 12, 2319-2338. [Google Scholar] [CrossRef]
|
|
[2]
|
Braza, P.A. (2012) Predator-Prey Dynamics with Square Root Functional Responses. Nonlinear Analysis: Real World Applications, 13, 1837-1843. [Google Scholar] [CrossRef]
|
|
[3]
|
Ma, X.M., Shao, Y.F. and Wang, Z. (2016) An Impulsive Two-Stage Predator-Prey Model with Stage-Structure and Square Root Functional Responses. Mathematics and Computers in Simulation, 119, 91-107. [Google Scholar] [CrossRef]
|
|
[4]
|
Salman, S.M., Yousef, A.M. and Elsadany, A.A. (2016) Sta-bility, Bifurcation Analysis and Chaos Control of a Discrete Predator-Prey System with Square Root Functional Re-sponse. Chaos, Solitons & Fractals, 93, 20-31. [Google Scholar] [CrossRef]
|
|
[5]
|
Bulai, I.M. and Venturino, E. (2017) Shape Effects on Herd Behavior in Ecological Interacting Population Models. Mathematics and Computers in Simulation, 141, 40-55. [Google Scholar] [CrossRef]
|
|
[6]
|
Panja, P. (2020) Combine Effects of Square Root Functional Response and Prey Refuge on Predatorprey Dynamics. International Journal of Modelling and Simulation. [Google Scholar] [CrossRef]
|
|
[7]
|
Kuznetsov, Y.A. (2013) Elements of Applied Bifurcation Theory. Springer Science & Business Media, New York. [Google Scholar] [CrossRef]
|
|
[8]
|
Hale, J.K. and Kocak, H. (1991) Dynamics and Bifurcations. Springer, New York. [Google Scholar] [CrossRef]
|