Figure 6

Phase space of system (13) for \(\beta _{\epsilon 0R} + C_{\mathrm{det}} > 0\), \(\lambda > 0\), and \(0 < \epsilon < \epsilon _{0}(\lambda )\) (in particular \(\lambda + \epsilon (\alpha _{\epsilon 0R} \pm \beta _{\epsilon 0R}) > 0\)). There exist two fixed points \(\bar{\mathcal{S}}^{\pm }_{\mathrm{osc}}\), a stable node and a saddle point, respectively, which together with the unstable invariant manifold of the saddle point form the invariant curve \(\bar{\mathcal{T}}_{\epsilon }\). Due to the coupling term, there are only two fixed points on \(\bar{\mathcal{T}}_{\epsilon }\), whereas we had an infinite number in the unperturbed case. Notice that the dynamics on the s direction is always attracting