On the zeros of transcendental functions with applications to stability of delay differential equations with two delays

摘要

In this paper, we first establish a basic theorem on the zeros of general transcendental functions. Based on the basic theorem, we develop a decomposition technique to investigate the stability of some exponential polynomials, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts. The technique combines the D-decomposition and τ-decomposition methods so that it can be used to study differential equations with multiple delays. As an application, we study the stability and bifurcation of a scalar equation with two delays modeling compound optical resonators.