Hopf bifurcations in a three-species food chain system with multiple delays

Xiaoliang Xie, and Wen Zhang. "Hopf bifurcations in a three-species food chain system with multiple delays." Open Mathematics 15.1 (2017): 508-519. <http://eudml.org/doc/288131>.

@article{XiaoliangXie2017,
abstract = {This paper is concerned with a three-species Lotka-Volterra food chain system with multiple delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the stability of the positive equilibrium and existence of Hopf bifurcations are investigated. Furthermore, the direction of bifurcations and the stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.},
author = {Xiaoliang Xie, Wen Zhang},
journal = {Open Mathematics},
keywords = {Three-species food chain; Delay; Hopf bifurcation; Center manifold; Periodic solutions; three-species food chain; delay; center manifold; periodic solutions},
language = {eng},
number = {1},
pages = {508-519},
title = {Hopf bifurcations in a three-species food chain system with multiple delays},
url = {http://eudml.org/doc/288131},
volume = {15},
year = {2017},
}

TY - JOUR
AU - Xiaoliang Xie
AU - Wen Zhang
TI - Hopf bifurcations in a three-species food chain system with multiple delays
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 508
EP - 519
AB - This paper is concerned with a three-species Lotka-Volterra food chain system with multiple delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the stability of the positive equilibrium and existence of Hopf bifurcations are investigated. Furthermore, the direction of bifurcations and the stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results.
LA - eng
KW - Three-species food chain; Delay; Hopf bifurcation; Center manifold; Periodic solutions; three-species food chain; delay; center manifold; periodic solutions
UR - http://eudml.org/doc/288131
ER -