Kuramoto model for excitation-inhibition-based oscillations

Abstract

The Kuramoto model (KM) is a theoretical paradigm for investigating the emergence of rhythmic activity in large populations of oscillators. A remarkable example of rhythmogenesis is the feedback loop between excitatory (E) and inhibitory (I) cells in large neuronal networks. Yet, although the EI-feedback mechanism plays a central role in the generation of brain oscillations, it remains unexplored whether the KM has enough biological realism to describe it. Here we derive a two-population KM that fully accounts for the onset of EI-based neuronal rhythms and that, as the original KM, is analytically solvable to a large extent. Our results provide a powerful theoretical tool for the analysis of large-scale neuronal oscillations.

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• Synchronization scenarios in the Winfree model of coupled oscillators
• Coupled networks and networks with bimodal frequency distributions are equivalent

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• Phase-Amplitude Coupling in Neuronal Oscillator Networks
• The Winfree model with heterogeneous phase-response curves: Analytical results
• Coupled Moebius Maps as a Tool to Model Kuramoto Phase Synchronization
• Volcano transition in populations of phase oscillators with random nonreciprocal interactions
• The XY model with vision cone: non-reciprocal vs. reciprocal interactions
• Collective dynamics of random Janus oscillator networks
• The Sakaguchi-Kuramoto model in presence of asymmetric interactions that break phase-shift symmetry
• The Winfree model with non-infinitesimal phase-response curve: Ott-Antonsen theory
• Solving the Kinetic Ising Model with Non-Reciprocity
• Finite-size scaling and dynamics in a two-dimensional lattice of identical oscillators with frustrated couplings
• Emergent synchrony in oscillator networks with adaptive arbitrary-order interactions
• Efficient moment-based approach to the simulation of infinitely many heterogeneous phase oscillators
• Synchronization modes in bipartite oscillator networks
• Sandpile cascades on oscillator networks: the BTW model meets Kuramoto