Zeros of a class of transcendental equation with application to bifurcation of DDE

Kit Ian Kou, Yijun Lou, Yong Hui Xia

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)

Abstract

Zeros of a class of transcendental equation with small parameter ϵ(0 ≤ ϵ ≤ 1) are considered in this paper. There have been many works in the literature considering the distribution of zeros of the transcendental equation by choosing the delay τ as bifurcation parameter. Different from standard consideration, we choose ϵ as bifurcation parameter (not the delay τ) to discuss the distribution of zeros of such transcendental equation. After mathematical analysis, the obtained results are successfully applied to the bifurcation analysis in a biological model in the real word phenomenon. In the real world model, the effect of climate changes can be seen as the small parameter perturbation, which can induce bifurcations and instability. We present two methods to analyze the stability and bifurcations.
Original languageEnglish
Article number1650062
JournalInternational Journal of Bifurcation and Chaos
Volume26
Issue number4
DOIs
Publication statusPublished - 1 Apr 2016

Keywords

  • characteristic equation
  • Hopf bifurcation
  • stability

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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