Our discovery opens pathways for subsequent research: what are the origins of the phase chimera? what other states are yet to be discovered in this system of globally coupled identical oscillators? and, of course, do states such as this emerge in naturally occurring systems?

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 story of this discovery started as many others do - by accident. While performing numerical simulations to investigate another question in this system, we came across a state that looked surprising at first and which we later identified as the "phase chimera state."

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.

Since we posted the findings on arxiv in 2023, these states have already been found in higher-order systems: journals.aps.org/pre/abstract..., arxiv.org/abs/2506.12511, link.springer.com/article/10.1...
@physreve.bsky.social

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.

If you are interested in participating in the workshop, please fill out the registration form available at the link below. The Zoom link for the meeting will be shared by email to all registered participants.
docs.google.com/forms/d/e/1F...