38 citations · 191 across the 14 of their papers we have counts for
14 papers
Self-organizing Chimera States in Adaptive Networks
Felix Augustsson, Rok Cestnik, Matthias Wolfrum +3
We propose a minimal adaptive network model with product-form coupling that reduces dimensionality while capturing key features of synaptic plasticity. The system spontaneously sel…
Two-phase quadratic integrate-and-fire neurons: Exact low-dimensional description for ensembles of finite-voltage neurons
Rok Cestnik
We introduce a two-phase quadratic integrate-and-fire (QIF) neuron whose membrane potential evolves according to two alternating Riccati equations within finite bounds. This simple…
Exact Dimensional Reduction for Quasi-Linear ODE Ensembles
Felix Augustsson, Erik Andreas Martens, Rok Cestnik
We present an exact dimensional reduction for high-dimensional dynamical systems composed of identical dynamical units governed by quasi-linear ordinary differential equations…
Next-Generation Reservoir Computing for Dynamical Inference
Rok Cestnik, Erik A. Martens
We present a simple and scalable implementation of next-generation reservoir computing (NGRC) for modeling dynamical systems from time-series data. The method uses a pseudorandom n…
Low Dimensional Dynamics of Globally Coupled Complex Riccati Equations: Exact Firing-rate Equations for Spiking Neurons with Clustered Substructure
Diego Pazó, Rok Cestnik
We report on an exact theory for ensembles of globally coupled, heterogeneous complex Riccati equations. A drastic dimensionality reduction to a few ordinary differential equations…
Continuum limit of the adaptive Kuramoto model
Rok Cestnik, Erik A. Martens
We investigate the dynamics of the adaptive Kuramoto model with slow adaptation in the continuum limit, . This model is distinguished by dense multistability, where mul…
Integrability of a globally coupled complex Riccati array: quadratic integrate-and-fire neurons, phase oscillators and all in between
Rok Cestnik, Erik A. Martens
We present an exact dimensionality reduction for dynamics of an arbitrary array of globally coupled complex-valued Riccati equations. It generalizes the Watanabe-Strogatz theory [P…
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…
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…
Inferring oscillator's phase and amplitude response from a scalar signal exploiting test stimulation
Rok Cestnik, Erik T. K. Mau, Michael Rosenblum
The phase sensitivity curve or phase response curve (PRC) quantifies the oscillator's reaction to stimulation at a specific phase and is a primary characteristic of a self-sustaine…
Hierarchy of exact low-dimensional reductions for populations of coupled oscillators
Rok Cestnik, Arkady Pikovsky
We consider an ensemble of phase oscillators in the thermodynamic limit, where it is described by a kinetic equation for the phase distribution density. We propose an ansatz for th…
Inferring the dynamics of oscillatory systems using recurrent neural networks
Rok Cestnik, Markus Abel
We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems pertur…
Inferring the phase response curve from observation of a continuously perturbed oscillator
Rok Cestnik, Michael Rosenblum
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for det…
Reconstructing networks of pulse-coupled oscillators from spike trains
Rok Cestnik, Michael Rosenblum
We present an approach for reconstructing networks of pulse-coupled neuron-like oscillators from passive observation of pulse trains of all nodes. It is assumed that units are desc…