Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9503300 | Journal of Mathematical Analysis and Applications | 2005 | 21 Pages |
Abstract
We consider a delayed predator-prey system. We first consider the existence of local Hopf bifurcations, and then derive explicit formulas which enable us to determine the stability and the direction of periodic solutions bifurcating from Hopf bifurcations, using the normal form theory and center manifold argument. Special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu [Trans. Amer. Math. Soc. 350 (1998) 4799], we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations supporting the theoretical analysis are also given.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yongli Song, Junjie Wei,