Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays
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Authors
Dingyang Lv
- Department of Mathematics, Hunan First Normal College, Changsha, 410205 Hunan, P. R. China.
Wen Zhang
- School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205 Hunan, P. R. China.
- School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. China.
Yi Tang
- Department of Mathematics, Hunan First Normal College, Changsha, 410205 Hunan, P. R. China.
Abstract
In this paper, we consider a ratio-dependent predator-prey system with multiple delays where the dynamics
are logistic with the carrying capacity proportional to prey population. By choosing the sum \(\tau\)
of two delays as the bifurcation parameter, the stability of the positive equilibrium and the existence of
Hopf bifurcation are investigated. Furthermore, the direction of Hopf bifurcation and the stability of the
bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem
for functional differential equations. Finally, some numerical simulations are carried out for illustrating the
theoretical results.
Share and Cite
ISRP Style
Dingyang Lv, Wen Zhang, Yi Tang, Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 3479--3490
AMA Style
Lv Dingyang, Zhang Wen, Tang Yi, Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays. J. Nonlinear Sci. Appl. (2016); 9(6):3479--3490
Chicago/Turabian Style
Lv, Dingyang, Zhang, Wen, Tang, Yi. "Bifurcation analysis for a ratio-dependent predator-prey system with multiple delays." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 3479--3490
Keywords
- Ratio-dependent
- delay
- Hopf bifurcation
- center manifold
- periodic solutions.
MSC
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