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Stability and bifurcation of numerical discretization of a second-order delay differential equation with negative feedback

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  • Ding, Xiaohua
  • Su, Huan
  • Liu, Mingzhu

Abstract

The paper analyzes a discrete second-order, nonlinear delay differential equation with negative feedback. The characteristic equation of linear stability is solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The existence of local Hopf bifurcations is investigated, and the direction and stability of periodic solutions bifurcating from the Hopf bifurcation of the discrete model are determined by the Hopf bifurcation theory of discrete system. Finally, some numerical simulations are performed to illustrate the analytical results found.

Suggested Citation

  • Ding, Xiaohua & Su, Huan & Liu, Mingzhu, 2008. "Stability and bifurcation of numerical discretization of a second-order delay differential equation with negative feedback," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 795-807.
    • Handle: RePEc:eee:chsofr:v:35:y:2008:i:4:p:795-807
    DOI: 10.1016/j.chaos.2006.05.055
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