4 papers
Predicting the occurrence of Braess paradox in the synchronization threshold of coupled oscillator systems
Justin Arches, Emmanuel Fleurantin, Matt Holzer +2
We study Braess-type paradoxes in coupled oscillator networks where the addition of an edge to the network leads to an increase in the critical coupling required for the existence…
Rate-Induced Tipping in a Non-Uniformly Moving Habitat and Determination of the Critical Rate
Blake Barker, Emmanuel Fleurantin, Matt Holzer +2
A habitat that is moving due to environmental change may result in tipping to extinction if the rate at which it moves is too great. We use a scalar reaction-diffusion equation wit…
Capturing the critical coupling of large random Kuramoto networks with graphons
Jason Bramburger, Matt Holzer
Collective oscillations and patterns of synchrony have long fascinated researchers in the applied sciences, particularly due to their far-reaching importance in chemistry, physics,…
Persistence of steady-states for dynamical systems on large networks
Jason J. Bramburger, Matt Holzer, Jackson Williams
The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the a…