IJPAM: Volume 99, No. 2 (2015)

DOUBLE HOPF BIFURCATION FOR AN HOPFIELD
EURAL NETWORK MODEL WITH TIME
DELAYED FEEDBACK

M.H. Moslehi$^1$, H.M. Mohammadinejad$^2$, O. Rabiei Motlagh$^3$
$^{1,2,3}$Department of Mathematics
University of Birjand
Birjand, IRAN
$^1$Department of Mathematics
Payame Noor University
Birjand, IRAN


Abstract. In this paper, we consider a system of delay differential equations which represents the general model of a Hopfield neural networks type. We focus on the case that the corresponding linear system has two pairs of purely imaginary eigenvalues at the trivial equilibrium, giving rise to double Hopf bifurcations. An analytical approach is used to find the explicit expressions for the critical values of the system parameters at which nonresonant or resonant double Hopf bifurcations may occur. We also investigate the occurrence of an double Hopf bifurcation about the trivial equilibrium.

Received: October 14, 2014

AMS Subject Classification: 34K06, 37H20, 70K30, 74G10, 93B52

Key Words and Phrases: Hopfield neural networks, Delayed differential equation, Double Hopf bifurcation

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DOI: 10.12732/ijpam.v99i2.5 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: 2015
Volume: 99
Issue: 2
Pages: 177 - 189


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