Stability and Hopf bifurcation analysis of a ratio-dependent predator–prey model with two time delays and Holling type III functional response
Xuedi Wang,
Miao Peng and
Xiuyu Liu
Applied Mathematics and Computation, 2015, vol. 268, issue C, 496-508
Abstract:
In this paper, a delayed ratio-dependent predator–prey model with Holling type III functional response and stage structure for the predator is considered. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of Hopf bifurcations at the coexistence equilibrium is established. By utilizing normal form method and center manifold theorem, the explicit formulas which determine the direction of Hopf bifurcation and the stability of bifurcating period solutions are derived. Finally, numerical simulations supporting the theoretical analysis are given.
Keywords: Predator–prey system; Ratio-dependent; Local stability; Hopf bifurcation (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315008899
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:496-508
DOI: 10.1016/j.amc.2015.06.108
Access Statistics for this article
Applied Mathematics and Computation is currently edited by Theodore Simos
More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().