Hopf Bifurcations in a Predator-Prey System of Population Allelopathy with Discrete DelayReport as inadecuate




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A delayed Lotka-Volterra two-species predator-prey system of population allelopathy with discrete delay is considered. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcations are demonstrated. 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 FDEs. Finally, some numerical simulations are carried out for illustrating the theoretical results.

KEYWORDS

Lotka-Volterra Predator-Prey System; Discrete Delay; Allelopathy; Stability; Hopf Bifurcation; Periodic Solution

Cite this paper

X. Wang and H. Liu -Hopf Bifurcations in a Predator-Prey System of Population Allelopathy with Discrete Delay,- Applied Mathematics, Vol. 3 No. 6, 2012, pp. 652-661. doi: 10.4236-am.2012.36099.





Author: Xinhui Wang, Haihong Liu

Source: http://www.scirp.org/



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