Stability and bifurcation analysis of a discrete predator-prey model with Holling type III functional response
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Authors
Jiangang Zhang
- Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Tian Deng
- Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Yandong Chu
- Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Shuang Qin
- Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Wenju Du
- School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
Hongwei Luo
- Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu, 730070, China.
- Department of Information Engineering, Gansu forestry technological College, Tianshui, Gansu 741020, China.
Abstract
The paper studies the dynamical behaviors of a discrete predator-prey system with Holling type III
functional response. More precisely, we investigate the local stability of equilibriums,
flip bifurcation and
Neimark-Sacker bifurcation of the model by using the center manifold theorem and the bifurcation theory.
And analyze the dynamic characteristics of the system in two-dimensional parameter-spaces, one can observe
the ''cluster'' phenomenon. Numerical simulations not only illustrate our results, but also exhibit the complex
dynamical behaviors of the model. The results show that we can more clearly and directly observe the chaotic
phenomenon, period-adding and Neimark-Sacker bifurcation from two-dimensional parameter-spaces and the
optimal parameters matching interval can also be found easily.
Share and Cite
ISRP Style
Jiangang Zhang, Tian Deng, Yandong Chu, Shuang Qin, Wenju Du, Hongwei Luo, Stability and bifurcation analysis of a discrete predator-prey model with Holling type III functional response, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 6228--6243
AMA Style
Zhang Jiangang, Deng Tian, Chu Yandong, Qin Shuang, Du Wenju, Luo Hongwei, Stability and bifurcation analysis of a discrete predator-prey model with Holling type III functional response. J. Nonlinear Sci. Appl. (2016); 9(12):6228--6243
Chicago/Turabian Style
Zhang, Jiangang, Deng, Tian, Chu, Yandong, Qin, Shuang, Du, Wenju, Luo, Hongwei. "Stability and bifurcation analysis of a discrete predator-prey model with Holling type III functional response." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 6228--6243
Keywords
- Predator-prey system
- stability
- flip bifurcation
- Neimark-Sacker bifurcation
- cluster
- parameter-space.
MSC
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