Proving the stability of the phase chimera state was its own journey, with detours including the consultation at the Sorbonne library in Paris, France of a 1997 PhD thesis which was not available digitally. Read more in the "historical notes" section of the supplementary material!

The Stuart-Landau system is still full of secrets waiting to be discovered. It is rich not only in its dynamics, but in its potential for beautiful visualizations. In fact, here is the winning image from the @aps-dsnp.bsky.social image of the month competition.

Last, but certainly not least, the phase chimera state, which is obtained here from perturbing a two-cluster state

Next, the incoherent state, whose region of existence in the parameter space overlaps with the phase chimera, and is found under different initial conditions:

Just for fun (and visual pleasure), here are videos of several of the states. First up, chaos! More are available here: pubs.aip.org/aip/cha/arti...

The Stuart-Landau system of globally coupled, identical oscillators displays rich dynamics from synchrony to clusters, chimeras, and chaos, despite only having three parameters (yay, nonlinear dynamics!)

In this paper, we show the existence and stability of a new class of chimera states: the "phase chimera" and "multitailed phase chimera." These states, discovered in the Stuart-Landau system of identical, globally coupled oscillators, are frozen in a co-rotating frame.