426 citations · 3.8k across the 126 of their papers we have counts for
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Exact finite-dimensional description for networks of globally coupled spiking neurons
Bastian Pietras, Rok Cestnik, Arkady Pikovsky
We consider large networks of globally coupled spiking neurons and derive an exact low-dimensional description of their collective dynamics in the thermodynamic limit. Individual n…
Traveling chimeras in oscillator lattices with advective-diffusive coupling
L. Smirnov, A. Pikovsky
We consider a one-dimensional array of phase oscillators coupled via an auxiliary complex field. While in the seminal chimera studies by Kumamoto and Battogtokh only diffusion of t…
Exact finite-dimensional reduction for a population of noisy oscillators and its link to Ott-Antonsen and Watanabe-Strogatz theories
Rok Cestnik, Arkady Pikovsky
Populations of globally coupled phase oscillators are described in the thermodynamic limit by kinetic equations for the distribution densities, or equivalently, by infinite hierarc…
Chaos in Coupled Heteroclinic Cycles and its Piecewise-Constant Representation
Arkady Pikovsky, Alexander Nepomnyashchy
We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical expl…