Fig. 5

Codimension-two bifurcation diagrams showing the stability regions for the swimming (light grey and red) and synchrony (light red) limit cycles under variation of (\(w_{\mathrm{inh}}\), \(w_{\mathrm{ampa}}\)) in (A) and (\(w_{\mathrm{inh}}\), \(w_{\mathrm{nmda}}\)) in (B). Superscripts − and + refer to subcritical and supercritical bifurcations, respectively. To clarify the stability of the limit cycles for low values of \(w_{\mathrm{ampa}}\), we computed the codimension-one bifurcation diagram at fixed value \(w_{\mathrm{ampa}} =10\) nS shown in Fig. 6 (orange dotted line). Bifurcation points B and D switch the criticality of the PD bifurcation (subcritical to supercritical). The LPD point is a fold-flip bifurcation point. At this point, a pitchfork bifurcation curve (PFK, blue line) interacts with a PD line and both exchange criticality