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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access November 24, 2015

Computation of double Hopf points for delay differential equations

  • Yingxiang Xu and Tingting Shi
From the journal Open Mathematics

Abstract

Relating to the crucial problem of branch switching, the calculation of codimension 2 bifurcation points is one of the major issues in numerical bifurcation analysis. In this paper, we focus on the double Hopf points for delay differential equations and analyze in detail the corresponding eigenspace, which enable us to obtain the finite dimensional defining system of equations of such points, instead of an infinite dimensional one that happens naturally for delay systems. We show that the double Hopf point, together with the corresponding eigenvalues, eigenvectors and the critical values of the bifurcation parameters, is a regular solution of the finite dimensional defining system of equations, and thus can be obtained numerically through applying the classical iterative methods. We show our theoretical findings by a numerical example.

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Received: 2015-8-6
Accepted: 2015-11-6
Published Online: 2015-11-24

©2015 Xu and Shi

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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