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

• Autorzy: Xiaoliang Xie , Wen Zhang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Three-species food chain; Delay; Hopf bifurcation; Center manifold; Periodic solutions

Kategorie tematyczne

• 34C23: Bifurcation
• 34C25: Periodic solutions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 508-519

Daty

wydano

2017-01-01

otrzymano

2016-11-02

zaakceptowano

2017-02-07

online

2017-04-26

Twórcy

autor

Xiaoliang Xie

• School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205, Hunan,
• Key Laboratory of Hunan Province for Mobile Business Intelligence, Hunan University of Commerce, Changsha 410205, Hunan,

autor

Wen Zhang

• School of Mathematics and Statistics, Hunan University of Commerce, Changsha, 410205, Hunan,

Identyfikatory

DOI

10.1515/math-2017-0039