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

Author

Listed:
  • Sun, Chengjun
  • Lin, Yiping
  • Han, Maoan
  • Tang, Shoupeng

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.

Suggested Citation

  • Sun, Chengjun & Lin, Yiping & Han, Maoan & Tang, Shoupeng, 2007. "Analysis for a special first order characteristic equation with delay dependent parameters," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 388-395.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:2:p:388-395
    DOI: 10.1016/j.chaos.2005.12.031
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    References listed on IDEAS

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    1. Ji, J.C. & Hansen, Colin H., 2005. "Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 461-473.
    2. Yang, Hong-Yong & Tian, Yu-Ping, 2005. "Hopf bifurcation in REM algorithm with communication delay," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1093-1105.
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