Many biological and neural systems can be seen as networks of interacting periodic
processes. Importantly, their functionality, ie, whether these networks can perform their …

Synchronization occurs in many natural and technological systems, from cardiac pacemaker
cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the …

A major goal of neuroscience, statistical physics, and nonlinear dynamics is to understand
how brain function arises from the collective dynamics of networks of spiking neurons. This …

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 …

Theta-nested gamma oscillations have been reported in many areas of the brain and are
believed to represent a fundamental mechanism to transfer information across spatial and …

Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and
incoherent domains and can be observed in networks of coupled oscillators. The interplay of …

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and
technology. For example, adaptive couplings appear in various real-world systems, such as …

We develop an approach for the description of the dynamics of large populations of phase
oscillators based on “circular cumulants” instead of the Kuramoto-Daido order parameters …

Electrical synapses play a major role in setting up neuronal synchronization, but the precise
mechanisms whereby these synapses contribute to synchrony are subtle and remain …

Recurrently coupled networks of inhibitory neurons robustly generate oscillations in the
gamma band. Nonetheless, the corresponding Wilson-Cowan type firing rate equation for …