Ring of identical cells with delayed coupling

doi:10.1088/0951-7715/18/6/022

Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling

Sue Ann Campbell et al 2005 Nonlinearity 18 2827-2846 doi: 10.1088/0951-7715/18/6/022

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Sue Ann Campbell^1,2, Yuan Yuan³ and Sharene D Bungay^1,4
¹ Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
² Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montréal, QC, H3G 1Y6, Canada
³ Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland, A1C 5S7, Canada
⁴ Current address: Department of Computer Science, Memorial University of Newfoundland, St John's, Newfoundland, A1C 5S7, Canada.
E-mail: sacampbell@uwaterloo.ca

Recommended by D Treschev

Abstract. We consider a ring of identical elements with time delayed, nearest-neighbour coupling. The individual elements are modelled by a scalar delay differential equation which includes linear decay and nonlinear delayed feedback. The bifurcation and stability of nontrivial asynchronous oscillations from the trivial solution are analysed using equivariant bifurcation theory and centre manifold construction.

Mathematics Subject Classification: 34K17, 37G40, 92B20

Print publication: Issue 6 (November 2005)
Received 21 June 2005, in final form 7 September 2005
Published 7 October 2005

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Equivariant Hopf bifurcation in a ring of identical cells with delayed coupling

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