  We discuss synchronization patterns in networks of FitzHugh-Nagumo and Leaky
Integrate-and-Fire oscillators coupled in a two-dimensional toroidal geometry.
Common feature between the two models is the presence of fast and slow
dynamics, a typical characteristic of neurons. Earlier studies have
demonstrated that both models when coupled nonlocally in one-dimensional ring
networks produce chimera states for a large range of parameter values. In this
study, we give evidence of a plethora of two-dimensional chimera patterns of
various shapes including spots, rings, stripes, and grids, observed in both
models, as well as additional patterns found mainly in the FitzHugh-Nagumo
system. Both systems exhibit multistability: For the same parameter values,
different initial conditions give rise to different dynamical states.
Transitions occur between various patterns when the parameters (coupling range,
coupling strength, refractory period, and coupling phase) are varied. Many
patterns observe in the two models follow similar rules. For example the
diameter of the rings grows linearly with the coupling radius.
