Chimera states are self-organized spatiotemporal patterns of coexisting coherence and
incoherence. We give an overview of the main mathematical methods used in studies of …

Kuramoto oscillators are widely used to explain collective phenomena in networks of
coupled oscillatory units. We show that simple networks of two populations with a generic …

The simplest network of coupled phase-oscillators exhibiting chimera states is given by two
populations with disparate intra-and inter-population coupling strengths. We explore the …

We consider the effect of small independent local noise on a network of quadratic integrate-
and-fire neurons, globally coupled via synaptic pulses of finite width. The Fokker-Planck …

We analyze the dynamics of a large network of coupled quadratic integrate-and-fire
neurons, which represent the canonical model for class I neurons near the spiking threshold …

Chimeras occur in networks of coupled oscillators and are characterized by coexisting
groups of synchronous oscillators and asynchronous oscillators. We consider a network …

We consider chimera states in a one-dimensional medium of nonlinear nonlocally coupled
phase oscillators. In terms of a local coarse-grained complex order parameter, the problem …

We consider a large network of globally coupled quadratic integrate-and-fire neurons, which
are canonical representatives for class I neurons near the spiking threshold. The model …

Synchronized oscillators are ubiquitous in nature and engineering. Despite several models
that have been proposed to treat synchronized oscillators beyond weak coupling, the widely …

We consider the macroscopic regimes and the scenarios for the onset and the suppression
of collective oscillations in a heterogeneous population of active rotators composed of …