Degenerated Hopf bifurcation in the Fitzhugh-Nagumo system. 2. Bautin bifurcation

Authors

  • Carmen Rocşoreanu University of Craiova, Romania
  • Nicolaie Giurgiţeanu University of Craiova, Romania
  • Adelina Georgescu Institute of Applied Mathematics, Romanian Academy, Romania

DOI:

https://doi.org/10.33993/jnaat291-659
Abstract views: 184

Abstract

The results on the Hopf bifurcation obtained in [1] are completed with those concerning the degenerated Hopf bifurcation of Bautin type. They are deduced by normal forms technique and concern a biodynamical system related with Van der Pol oscillator. Numerical investigations carried out by methods from [2] are also reported.

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References

Georgescu A., Rocşoreanu C., Giurgiţeanu N.-Equilibria and relaxation oscillations of the nodal system of the heart. 2. Hopf bifurcation, Rev. Roum. Sci.-Tech.Mec. Appl. (in press)

Giurgiţeanu N.- Study of the phase portrait. I. Improvements of the numerical methods, St. cerc. mec. apl., 55, 5-6, pp. 335-355, (1996). (Romanian)

Rocşoreanu C.-Equilibria and relaxation oscillations of the nodal system of the heart. 1. Bifurcation diagrams of equilibria, Rev. Roum. Sci.-Tech.Mec. Appl.43,no 3(1998)

Guckenheimer J., Holmes P.- Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Springer, New York, 1983, https://doi.org/10.1007/978-1-4612-1140-2 DOI: https://doi.org/10.1007/978-1-4612-1140-2

Kuznetsov, Yu., Elements of applied bifurcation theory, Springer, New York, 1995, https://doi.org/10.1007/978-1-4757-2421-9 DOI: https://doi.org/10.1007/978-1-4757-2421-9

Rocşoreanu C., Giurgiţeanu N., Georgescu A. - Degenerated Hopf bifurcation in the FitzHugh-Nagumo system. 1. Bogdanov-Takens bifurcation, Ann. of Univ. of Timişoara, XXXV, (2), (1997), pp. 285-298.

*** Mathematica, A system for doing mathematics by computer, 1994

Rocşoreanu, C. (1997) Dynamics and bifurcation in the FitzHugh-Nagumo equation, Romanian Academy, Bucharest, PhD Thesis (Romanian).

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Published

2000-02-01

How to Cite

Rocşoreanu, C., Giurgiţeanu, N., & Georgescu, A. (2000). Degenerated Hopf bifurcation in the Fitzhugh-Nagumo system. 2. Bautin bifurcation. Rev. Anal. Numér. Théor. Approx., 29(1), 97–109. https://doi.org/10.33993/jnaat291-659

Issue

Vol. 29 No. 1 (2000)

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Articles

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