305 citations · 325 across the 9 of their papers we have counts for
9 papers
Phase oscillator networks with multiple and state-dependent delays: A framework for exploring white matter plasticity in neurodynamics
Grace Jolly, Rachel Nicks, Stefan Ruschel +2
Network science is increasingly focused on how node dynamics influence emergent phenomena such as oscillations, waves, chimeras, and turbulence. In oscillatory systems modeled by n…
Adaptive conduction delays and phase locking in spiking Haken Lighthouse networks
Stephen Coombes, Rüdiger Thul, Stefan Ruschel +1
We develop a theory of phase-locked activity in delayed spiking networks using the Haken Lighthouse model as an analytically tractable event-based description of neural dynamics. F…
Network Attractors driven by Time-Delay Plasticity
Stefan Ruschel, Emanuil Hristov, Hil G. E. Meijer +2
We develop a framework for collective frequency selection and attractor formation by means of delay plasticity. Specifically, we consider adaptive axonal delays (AADs), motivated b…
Phase and amplitude responses for delay equations using harmonic balance
Rachel Nicks, Robert Allen, Stephen Coombes
Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary d…
Insights into oscillator network dynamics using a phase-isostable framework
Rachel Nicks, Robert Allen, Stephen Coombes
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled os…
Oscillatory networks: Insights from piecewise-linear modeling
Stephen Coombes, Mustafa Sayli, Rüdiger Thul +3
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such net…
Clusters in nonsmooth oscillator networks
Rachel Nicks, Lucie Chambon, Stephen Coombes
For coupled oscillator networks with Laplacian coupling the master stability function (MSF) has proven a particularly powerful tool for assessing the stability of the synchronous s…
Mathematical frameworks for oscillatory network dynamics in neuroscience
Peter Ashwin, Stephen Coombes, Rachel Nicks
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 ce…
A classification of the symmetries of uniform discrete defective crystals
Rachel Nicks
Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are…