207 citations · 425 across the 7 of their papers we have counts for
7 papers
Is the Ott-Antonsen manifold attracting?
Jan R. Engelbrecht, Renato Mirollo
The Kuramoto model is a paradigm for studying oscillator networks with interplay between coupling tending towards synchronization, and heterogeneity in the oscillator population dr…
The Kuramoto model on a sphere: Explaining its low-dimensional dynamics with group theory and hyperbolic geometry
Max Lipton, Renato Mirollo, Steven H. Strogatz
We study a system of interacting particles moving on the unit sphere in -dimensional space. The particles are self-propelled and coupled all to all, and their motion is heav…
Dynamics of the Kuramoto-Sakaguchi Oscillator Network with Asymmetric Order Parameter
Bolun Chen, Jan R. Engelbrecht, Renato Mirollo
We study the dynamics of a generalized version of the famous Kuramoto-Sakaguchi coupled oscillator model. In the classic version of this system, all oscillators are governed by the…
Hyperbolic Geometry of Kuramoto Oscillator Networks
Bolun Chen, Jan R. Engelbrecht, Renato Mirollo
Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the Möbius group acting on the state space …
Phase oscillators with global sinusoidal coupling evolve by Mobius group action
Seth A. Marvel, Renato E. Mirollo, Steven H. Strogatz
Systems of N identical phase oscillators with global sinusoidal coupling are known to display low-dimensional dynamics. Although this phenomenon was first observed about 20 years a…
Dynamical Phase Transitions In Driven Integrate-And-Fire Neurons
Jan R. Engelbrecht, Renato Mirollo
We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron's natural firing period and that of…
The Spectrum of the Partially Locked State for the Kuramoto Model
Renato Mirollo, Steven H. Strogatz
We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fi…