Rocşoreanu, Carmen; Giurgiţeanu, Nicolaie; Georgescu, Adelina Connections between saddles for the FitzHugh-Nagumo system. (English) Zbl 1090.37549 Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, No. 2, 533-540 (2001). Summary: By studying the two-dimensional FitzHugh-Nagumo (F-N) dynamical system, points of Bogdanov-Takens bifurcation are detected. Two of the curves of homoclinic bifurcation emerging from these points intersect each other at a point of double breaking saddle-connection bifurcation. Numerical investigations of the bifurcation curves emerging from this point, in the parameter plane, allow us to find other types of codimension-one and -two bifurcations concerning the connections between saddles and saddle-nodes, referred to as saddle-node-saddle connection bifurcation and saddle-node-saddle with separatrix connection bifurcation, respectively. The local bifurcation diagrams corresponding to these bifurcations are presented. An analogy between the bifurcation corresponding to the point of double homoclinic bifurcation and the point of double breaking saddle connection bifurcation is presented, too. Cited in 4 Documents MSC: 37G20 Hyperbolic singular points with homoclinic trajectories in dynamical systems 37N25 Dynamical systems in biology PDFBibTeX XMLCite \textit{C. Rocşoreanu} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, No. 2, 533--540 (2001; Zbl 1090.37549) Full Text: DOI References: [1] DOI: 10.1016/S0006-3495(61)86902-6 · doi:10.1016/S0006-3495(61)86902-6 [2] Georgescu A., Dishliev, A. pp 33– (1997) [3] Hale J. K., Chap. 13 pp 401– (1991) [4] Kuznetsov Yu., Chap. 8 pp 272– (1995) [5] Rocşoreanu C., Ann. University of Timisoara XXXV-2 pp 285– (1997) [6] DOI: 10.1137/0518083 · Zbl 0651.58025 · doi:10.1137/0518083 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.