Fig. 6

Interaction between \(S^{a}_{\varepsilon }\) and \(S^{s}_{\varepsilon }\) in system (11) with \(\mu =100.1\) and \(\varepsilon =0.01\). Panel (a) shows \(S^{a}_{\varepsilon }\) (red) and \(S^{s}_{\varepsilon }\) (green) projected onto the \((x,y,z)\)-space, and computed up to the three-dimensional section Σ (blue); the gray surface is the critical manifold S and the gray line is the fold curve F. Panel (b) shows the intersection curves \(\widehat{S}^{a}_{\varepsilon } = S^{a}_{\varepsilon } \cup \varSigma \) (red) and \(\widehat{S}^{s}_{\varepsilon } = S^{s}_{\varepsilon } \cup \varSigma \) (green) in the (\(x,w,z\))-space of Σ. Panel (c1) shows the curves \(\widehat{S}^{a}_{\varepsilon ,z}\) (red) and \(\widehat{S}^{a}_{\varepsilon ,w}\) (orange) as projections of \(\widehat{S}^{a}_{\varepsilon }\) onto the \((x,z)\)- and \((x,w)\)-planes, respectively, together with the intersection curve \(\widehat{S}^{s}_{\varepsilon }\) (green), which is the same in both projections. Panel (c2) is an enlargement of panel (c1)