# IJPAM: Volume 109, No. 4 (2016)

HOPF BIFURCATION ANALYSIS AND DESIGN
OF HYBRID CONTROL FOR GROWTH MODEL WITH DELAY

Department of Mathematics
Faculty of Mathematics and Statistics
University of Birjand, Birjand, IRAN

Abstract. In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Hybrid controler to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a hybeid controller by setting proper controling parameter. Under consideration model as operator Equation, apply orthogonal decomposition, compute the center manifold and normal form we determined the direction and stability of bifurcating periodic solutions. Therefore the Hopf bifurcation of the model became controllable to achieve desirable behaviors which are applicable in certain circumstances.

Revised: September 18, 2016

Published: October 9, 2016

AMS Subject Classification: 34H20, 34D23

Key Words and Phrases: Hopf bifurcation, bifurcation control, hybrid control, stability, timedelay

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# .

DOI: 10.12732/ijpam.v109i4.6 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 4
Pages: 827 - 836