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Communications in Mathematical Biology and Neuroscience ISSN 2052-2541

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Commun. Math. Biol. Neurosci. 2015 (2015), Article ID 1

Hopf bifurcation in a delayed logistic growth with feedback control

Xiaojie Gong, Xianddong Xie, Rongyu Han, Liya Yang

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Abstract

In this paper, the bifurcation of the delayed logistic model with feedback control variable are investigated. By regarding the corresponding characteristic equations, the linear stability of the system is discussed and Hopf bifurcations are demonstrated, especially the stability switch is discussed in this system. By the normal form and the center manifold theory, the explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. Finally, some examples are presented to verify our main results.

Published
20 March 2015
Volume
2015 (2015)
License
CC BY 3.0

Copyright © 2015 Xiaojie Gong, Xianddong Xie, Rongyu Han, Liya Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

X. Gong, X. Xie, R. Han, L. Yang, Hopf bifurcation in a delayed logistic growth with feedback control, Commun. Math. Biol. Neurosci. 2015 (2015), 1.

BibTeX
@article{Gong2015,
  author  = {Gong, Xiaojie and Xie, Xianddong and Han, Rongyu and Yang, Liya},
  title   = {Hopf bifurcation in a delayed logistic growth with feedback control},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2015},
  year    = {2015},
  pages   = {1},
  doi     = {}
}