38 citations · 191 across the 14 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…
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…
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…