Dynamics of a predator-prey system with stage structure and two delays
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Authors
Juan Liu
- Department of Mathematics and Physics, Bengbu University, Bengbu 233030, P. R. China.
Zizhen Zhang
- School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, P. R. China.
Abstract
A Holling type III predator-prey system with stage structure for the predator and two delays is inves-
tigated. At first, we study the stability and the existence of periodic solutions via Hopf bifurcation with
respect to both delays at the positive equilibrium by analyzing the distribution of the roots of the associated
characteristic equation. Then, explicit formulas that can determine the direction of the Hopf bifurcation
and the stability of the periodic solutions bifurcating from the Hopf bifurcation are established by using the
normal form method and center manifold argument. Finally, some numerical simulations are carried out to
support the main theoretical results.
Share and Cite
ISRP Style
Juan Liu, Zizhen Zhang, Dynamics of a predator-prey system with stage structure and two delays, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 3074--3089
AMA Style
Liu Juan, Zhang Zizhen, Dynamics of a predator-prey system with stage structure and two delays. J. Nonlinear Sci. Appl. (2016); 9(5):3074--3089
Chicago/Turabian Style
Liu, Juan, Zhang, Zizhen. "Dynamics of a predator-prey system with stage structure and two delays." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 3074--3089
Keywords
- Delays
- Hopf bifurcation
- periodic solutions
- predator-prey system
- stability.
MSC
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