TY - JOUR
T1 - Hopf Bifurcation of Delayed Predator-Prey System with Reserve Area for Prey and in the Presence of Toxicity
AU - Zhang , Zizhen
AU - Chu , Yugui
AU - Zhang , Xin
JO - Communications in Mathematical Research 
VL - 2
SP - 161
EP - 170
PY - 2019
DA - 2019/12
SN - 34
DO - http://doi.org/10.13447/j.1674-5647.2018.02.08
UR - https://global-sci.org/intro/article_detail/cmr/13523.html
KW - delay, Hopf bifurcation, predator-prey system, periodic solution, toxicity
AB - <p style="text-align: justify;">A kind of three species delayed predator-prey system with reserve area
for prey and in the presence of toxicity is proposed in this paper. Local stability of
the coexistence equilibrium of the system and the existence of a Hopf bifurcation is
established by choosing the time delay as the bifurcation parameter. Explicit formulas to determine the direction and stability of the Hopf bifurcation are obtained by
means of the normal form theory and the center manifold theorem. Finally, we give
a numerical example to illustrate the obtained results.</p>