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R. E. Beardmore, “Double Singularity-Induced Bifurca- tion Points and Singular Hopf Bifurcations,” Dynamics and Stability of Systems, Vol. 15, No. 4, 2000, pp. 319-342.

has been cited by the following article:

• TITLE: Singular Hopf Bifurcations in DAE Models of Power Systems

  AUTHORS: Wieslaw Marszalek, Zdzislaw Trzaska

  KEYWORDS: Power Systems, Singularly Perturbed Systems, DAEs, Bifurcations, Matrix Pencils

  JOURNAL NAME: Energy and Power Engineering, Vol.3 No.1, February 25, 2011

  ABSTRACT: We investigate an important relationship that exists between the Hopf bifurcation in the singularly perturbed nonlinear power systems and the singularity induced bifurcations (SIBs) in the corresponding different- tial-algebraic equations (DAEs). In a generic case, the SIB phenomenon in a system of DAEs signals Hopf bifurcation in the singularly perturbed systems of ODEs. The analysis is based on the linear matrix pencil theory and polynomials with parameter dependent coefficients. A few numerical examples are included.