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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Asymptotic Analysis of the Hopf-Hopf Bifurcation in a Time-delay System

Journal of Applied Nonlinear Dynamics 1(2) (2012) 159--171 | DOI:10.5890/JAND.2012.05.004

Christoffer R. Heckman$^{1}$; Richard H. Rand$^{2}$

$^{1}$ Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA

$^{2}$ Dept. Mathematics, Dept. MAE, Cornell University, Ithaca, NY 14853, USA

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A delay differential equation (DDE) which exhibits a double Hopf or Hopf-Hopf bifurcation [1] is studied using both Lindstedt’s method and center manifold reduction. Results are checked by comparison with a numerical continuation program (DDEBIFTOOL). This work has application to the dynamics of two interacting microbubbles.


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