Figure 16

Bifurcation diagram with parameters \(\mathcal{P}\) and \(b_{\mathrm{sp}}=0\) in (47) (corresponding to the “degenerated case” in Section 4.3). (A): Two-parameter bifurcation diagram where curves are the locus of bifurcations in the \((\mu ,\epsilon )\)-plane. The legend indicates bifurcations of a fixed point (FP) or a limit cycle (LC) giving rise to or involving the \(\varDelta \varphi = 0\) in-phase (IP) or \(\varDelta \varphi = \pi \) anti-phase (AP) solution branches; PD: period doubling; PF: pitchfork. Text labels indicate the solutions that are stable in a given region, e.g. ‘IP+AP’ is a region with coexisting, stable IP and AP solutions. (B): One-parameter bifurcation diagram for fixed \(\epsilon =0.05\) showing the fixed point branch, IP branch and AP branch; dashed segments are unstable. The IP and AP branches bifurcation from the FP branch at a degenerate Hopf bifurcation (bullet). The AP branch loses stability in a pitchfork bifurcation (diamond)