Fig. 7

Homotopy step for detecting canard orbit \(\xi _{4}\) of system (11) with \(\mu =100.1\) and \(\varepsilon =0.01\). Panels (a) and (b) are projections onto the (\(y,z\))-plane and (\(x,z\))-plane, respectively, and show a family of orbit segments of \(S^{a}_{\varepsilon }\) that stay close to \(S^{s}_{\varepsilon }\) for a certain amount of time. The red orbit, which stays close to \(S^{s}_{\varepsilon }\) for the longest time, is identified as the canard orbit \(\xi _{4}\) that satisfies (30)