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

Shigui Ruan, Junjie Wei

Research output: Contribution to journalArticle

632 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)863-874
Number of pages12
JournalDynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Issue number6
StatePublished - Dec 1 2003



  • Bifurcation
  • Compound optical resonators
  • Delay differential equations
  • Stability
  • Transcendental polynomials

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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