TY - JOUR AU - Zhang, Jiangang AU - Lu, Jiarong AU - Du, Wenju AU - Chu, Yandong AU - Luo, Hongwei PY - 2017 TI - Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays JO - Journal of Nonlinear Sciences and Applications SP - 4181--4196 VL - 10 IS - 8 AB - Keeping the balance of nature is important, and it is very significant to effectively control the number of species for ecosystem stability. In this paper, we propose a tritrophic Hastings-Powell (HP) model with two different time delays, and the local stability of equilibrium, Hopf bifurcation, and the existence and uniqueness of the positive equilibrium are analyzed in detail. Besides, we obtain the stable conditions for the system and prove that Hopf bifurcation will occur when the delay pass through the critical value. And the stability and direction of the Hopf bifurcation are also investigated by using the center manifold theorem and normal form theorem. Finally, some numerical examples are given to illustrate the results. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.08.14 DO - 10.22436/jnsa.010.08.14 ID - Zhang2017 ER -