Analysis for a special first order characteristic equation with delay dependent parameters

Chengjun Sun, Yiping Lin, Maoan Han and Shoupeng Tang

Chaos, Solitons & Fractals, 2007, vol. 33, issue 2, 388-395

Abstract: In this paper, the characteristic equation a(τ)λ+b(τ)+c(τ)e−λτ+d(τ)e−2λτ=0 with delay τ dependent parameters is investigated. Sufficient and necessary conditions for the existence of a pair of purely imaginary roots are obtained by introducing the auxiliary equations. The crossing directions of eigenvalue curves through the imaginary axis as the delay τ increases are determined by the formulae.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:33:y:2007:i:2:p:388-395

DOI: 10.1016/j.chaos.2005.12.031

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