Stability and Bifurcation Analysis of Volterra Functional Equations in the Light of Suns and Stars

We show that the perturbation theory for dual semigroups (sun-star-calculus) that has proved useful for analyzing delay-differential equations is equally efficient for dealing with Volterra functional equations. In particular, we obtain both the stability and instability parts of the principle of linearized stability and the Hopf bifurcation theorem. Our results apply to situations in which the instability part has not been proved before. In applications to general physiologically structured populations even the stability part is new.