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Volume 17,     Number 1,     Spring 2009

 

HOPF BIFURCATION OF DELAY
DIFFERENTIAL EQUATIONS WITH DELAY
DEPENDENT PARAMETERS
GUIHONG FAN, MAUNG MIN-OO AND GAIL S. K. WOLKOWICZ

Abstract. When the associated characteristic equation for a model involving delay differential equations is a transcendental equation with constant or delay dependent coefficients, a standard requirement for Hopf bifurcation is the existence of a pair of pure imaginary roots for some value of the delay. We develop a method that can be applied to locate intervals where a pair of pure imaginary roots of any such second order transcendental equation with delay dependent coefficients are likely to exist for some value of the delay in the interval, and when they exist, how to find them. An example is given illustrating our approach.

 

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