Periodic solutions of planar systems with two delays

Shigui Ruan, Junjie Wei

Research output: Contribution to journal › Article

81 Citations (Scopus)

Abstract

In this paper, we consider a planar system with two delays: ẋ1(t) = -a0x1(t) + a1F1(x1(t - τ1), x2(t - τ2)), ẋ2(t) = -b0x2(t) + b1F2(x1(t - τ1), x2(t - τ2)). Firstly, linearized stability and local Hopf bifurcations are studied. Then, existence conditions for non-constant periodic solutions are derived using degree theory methods. Finally, a simple neural network model with two delays is analysed as an example.

Original languageEnglish (US)
Pages (from-to)1017-1032
Number of pages16
JournalRoyal Society of Edinburgh - Proceedings A
Volume129
Issue number5
StatePublished - 1999
Externally publishedYes

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Hopf bifurcation
Periodic Solution
Neural networks
Degree Theory
Local Bifurcations
Neural Network Model
Hopf Bifurcation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Periodic solutions of planar systems with two delays. / Ruan, Shigui; Wei, Junjie.

In: Royal Society of Edinburgh - Proceedings A, Vol. 129, No. 5, 1999, p. 1017-1032.

Research output: Contribution to journal › Article

Ruan, S & Wei, J 1999, 'Periodic solutions of planar systems with two delays', Royal Society of Edinburgh - Proceedings A, vol. 129, no. 5, pp. 1017-1032.
Ruan S, Wei J. Periodic solutions of planar systems with two delays. Royal Society of Edinburgh - Proceedings A. 1999;129(5):1017-1032.
Ruan, Shigui ; Wei, Junjie. / Periodic solutions of planar systems with two delays. In: Royal Society of Edinburgh - Proceedings A. 1999 ; Vol. 129, No. 5. pp. 1017-1032.
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