Stability and Bifurcation in Delay–Differential Equations with Two Delays

AbstractThe purpose of this paper is to study a class of differential–difference equations with two delays. First, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. General stability criteria involving the delays and the parameters are obtained. Second, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits the Hopf bifurcation. The stability of the bifurcating periodic solutions are determined by using the center manifold theorem and the normal form theory. Finally, as an example, we analyze a simple motor control equation with two delays. Our results improve some of the existing results on this equation