5 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…
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…
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…
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…