Abstract
The 2-D FitzHugh-Nagumo (F-N) system depending on three real parameters a, b, and c is considered. It models the electrical potential of the nodal system in the heart. All local bifurcations of equilibria are emphasized in three qualitatively distinct situations concerning the parameter c(0 < c < 1, c = 1, c > 1). We found codimension-one bifurcations (saddle-node, Hopf), codimension two bifurcations (Bogdanov-Takens, Bautin, cusp, double-zero with order two symmetry) and a codimension three bifurcation (degenerated Bogdanov-Takens of order two). In addition, some non-generic codimension two bifurcations generated by the coexistence of two codimension one bifurcations are shown. In our study we used the normal form theory [3], [6] and the center manifold theory [2].
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35690-7_44
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Rocsoreanu, C., Sterpu, M. (2003). Local Bifurcation for the Fitzhugh-Nagumo System. In: Barbu, V., Lasiecka, I., Tiba, D., Varsan, C. (eds) Analysis and Optimization of Differential Systems. SEC 2002. IFIP — The International Federation for Information Processing, vol 121. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35690-7_35
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DOI: https://doi.org/10.1007/978-0-387-35690-7_35
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