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

The tools of weakly coupled phase oscillator theory have had a profound impact on the
neuroscience community, providing insight into a variety of network behaviours ranging from …

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 …

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 …

Large communities of biological oscillators show a prevalent tendency to self-organize in
time. This cooperative phenomenon inspired Winfree to formulate a mathematical model that …

The Wilson–Cowan population model of neural activity has greatly influenced our
understanding of the mechanisms for the generation of brain rhythms and the emergence of …

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 …

Recently, low-dimensional models of neuronal activity have been exactly derived for large
networks of deterministic, quadratic integrate-and-fire (QIF) neurons. Such firing rate models …