On the zeros of transcendental functions with applications to stability of delay differential equations with two delays
On the zeros of transcendental functions with applications to stability of delay differential equations with two delays
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发表时间：
2003-12
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通讯作者：
S. Ruan;Junjie Wei
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作者：
S. Ruan;Junjie Wei
本文首先建立了关于一般超越函数的零点的一个基本定理。在基本定理的基础上，我们发展了一种分解方法来研究一些指数多项式的稳定性，即找到指数多项式的所有零都有负实部的条件。该技术结合了d -分解和τ -分解方法，因此可以用于研究具有多重延迟的微分方程。作为一个应用，我们研究了一类双时延标量方程的稳定性和分岔问题。
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.