Figure 10
From: Exploring the geometry of the bifurcation sets in parameter space
Three-parameter plot showing codimension-one homoclinic \(hom^{(1,2)}\) bifurcation surfaces for the FitzHugh-Nagumo system. In plot (a) it is shown the theoretical structure of the homoclinic bifurcation surfaces, in this case it corresponds to the “duck-foot shape” case IIb of Fig. 5. Plots (b) and (c) show the homoclinic bifurcation curves for several values of the small parameter \(\varepsilon\) and the codimension-two Belyakov bifurcation curve obtained using the continuation software AUTO. Plot (b) is given in the three-parameter space \((\alpha , s, \varepsilon )\) while plot (c) is represented by using the parameters \((\alpha , \varepsilon )\) and the AUTO \(L_2\)-norm.
