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Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh–Nagumo system

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  • Algaba, A.
  • Fuentes, N.
  • Gamero, E.
  • García, C.

Abstract

We consider a class of three-dimensional systems having an equilibrium point at the origin, whose principal part is of the form (−∂h∂y(x,y),∂h∂x(x,y),f(x,y))T. This principal part, which has zero divergence and does not depend on the third variable z, is the coupling of a planar Hamiltonian vector field Xh(x,y):=(−∂h∂y(x,y),∂h∂x(x,y))T with a one-dimensional system.

Suggested Citation

  • Algaba, A. & Fuentes, N. & Gamero, E. & García, C., 2020. "Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh–Nagumo system," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308859
    DOI: 10.1016/j.amc.2019.124893
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    References listed on IDEAS

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    1. Algaba, A. & García, C. & Reyes, M., 2012. "Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 869-878.
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    Cited by:

    1. Xue, Miao & Gou, Junting & Xia, Yibo & Bi, Qinsheng, 2021. "Computation of the normal form as well as the unfolding of the vector field with zero-zero-Hopf bifurcation at the origin," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 377-397.
    2. Algaba, A. & Fuentes, N. & Gamero, E. & García, C., 2021. "On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier," Applied Mathematics and Computation, Elsevier, vol. 405(C).

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    1. Algaba, A. & Fuentes, N. & Gamero, E. & García, C., 2021. "On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier," Applied Mathematics and Computation, Elsevier, vol. 405(C).

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