Computation of double Hopf points for delay differential equations

• Autorzy: Yingxiang Xu , Tingting Shi
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

double Hopf points; delay differential equations; regular defining system of equations; iterative methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-08-06

zaakceptowano

2015-11-06

online

2015-11-24

Twórcy

autor

Yingxiang Xu

• School of Mathematics and Statistics, Northeast Normal University,

autor

Tingting Shi

• School of Mathematics and Statistics, Northeast Normal University,

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Identyfikatory

DOI

10.1515/math-2015-0076