Hopf bifurcation of sunflower equation parametrized by delay

If we choose r as a parameter, the dependence of F on r is complicated because renters the definition of z_t. Thus, we choose a as a parameter. It is well known that delayis the important factor to cause the differences between differential-difference and ordinarydifferential equations. So we choose the delay as a parameter for studying the bifurcationof delay differential equations. In this note, we investigate the Hopf bifurcation for