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Kuznetsov, Y.A. (2004) Elements of Applied Bifurcation Theory. 3rd Edition, Springer.

has been cited by the following article:

• TITLE: Generalized Hopf Bifurcation in a Delay Model of Neutrophil Cells Model

  AUTHORS: Suqi Ma, S. J. Hogan

  KEYWORDS: Generalized Hopf Bifurcation, DDE-Biftool Software, Norm Form

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.13 No.2, August 23, 2024

  ABSTRACT: The DDE-Biftool software is applied to solve the dynamical stability and bifurcation problem of the neutrophil cells model. Based on Hopf point finding with the stability property of the equilibrium solution loss, the continuation of the bifurcating periodical solution starting from Hopf point is exploited. The generalized Hopf point is tracked by seeking for the critical value of free parameter of the switching phenomena of the open loop, which describes the lineup of bifurcating periodical solutions from Hopf point. The normal form near the generalized Hopf point is computed by Lyapunov-Schimdt reduction scheme combined with the center manifold analytical technique. The near dynamics is classified by geometrically different topological phase portraits.