Publications

Roberto Garrappa, Katarzyna Górska, Eva Kaslik, Kateryna Marynets

Generalized fractional operators do not preserve periodicity

Fractional Calculus and Applied Analysis (FCAA)

This work allows proving that the action of fractional derivatives and fractional integrals on periodic functions does not preserve the periodicity of any period. This result is proved not only for one type of fractional operator but also…

Alexandru Fikl, Aman Jhinga, Eva Kaslik, Argha Mondal

Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models

Fractional Calculus and Applied Analysis (FCAA)

We introduce an efficient discretisation of a novel fractional-order adaptive exponential (FrAdEx) integrate-and-fire model, which is used to study the fractional-order dynamics of neuronal activities. The discretisation is based on an ex…

Anca Rădulescu, Eva Kaslik, Alexandru Fikl

Complex dynamics in two-dimensional coupling of quadratic maps

arXiv

This paper examines the structure and limitations of equi-M sets in two-dimensional Complex Quadratic Networks (CQNs). In particular, we aim to describe the relationship between the equi-M set and the parameter domains where the critical …

Anca Rădulescu, Eva Kaslik, Alexandru Fikl, Johan Nakuci, Sarah Muldoon, Michael Anderson

Fractal geometry predicts dynamic differences in structural and functional connectomes

arXiv

Understanding the intricate architecture of brain networks and its connection to brain function is essential for deciphering the underlying principles of cognition and disease. While traditional graph-theoretical measures have been widely…

Eva Kaslik, Maria Roxana Matei, Mihaela Neamțu, Anca Rădulescu

A time-delay model of dopamine-modulated prefrontal-limbic interactions in schizophrenia

In preparation

Alexandru Fikl

Adaptive step size controllers for fractional product integration methods

Fourth International Nonlinear Dynamics Conference (NODYCON 2025)

We propose an adaptive numerical algorithm for general nonlinear fractional initial value problems discretized using the popular Product Integration (PI) family of methods. The construction is based on rigorous error models for the rectan…

Diana Jianu

Performance analysis of ML architectures for predicting and classifying neural conditions using EEG datasets

Fourth International Nonlinear Dynamics Conference (NODYCON 2025)

Epilepsy is one of the most common neurological diseases in the world while multiple sclerosis (MS) is a rarer condition that affects a relatively small number of people. The fact that both affect the biosignals one's brain emits makes th…

Eva Kaslik

Networks of Wilson-Cowan nodes with distributed delays

Fourth International Nonlinear Dynamics Conference (NODYCON 2025)

We investigate the dynamics of Wilson-Cowan networks with distributed delays, initially focusing on networks with two nodes before extending our analysis to networks with an arbitrary number of nodes. Our primary aim is to understand the …

Mihaela Neamțu

Dynamics of a time-delay model of dopamine-modulated prefrontal-limbic interactions in schizophrenia

Fourth International Nonlinear Dynamics Conference (NODYCON 2025)

The paper analyzes a mathematical model of systemic degeneration in schizophrenia, described by a nonlinear differential system, where the time delay is introduced. The positivity of neural components of both the equilibrium and trajector…

Anca Rădulescu, Sarah Muldoon, Johan Nakuci, Eva Kaslik, Alexandru Fikl

Using complex dynamics to compute brain networks

Fourth International Nonlinear Dynamics Conference (NODYCON 2025)

The central goal of this work is to understand how global behavior in dynamic networks emerges from the interplay between the network's connectivity profile and the node-wise dynamics. We explore this direction with a novel modeling appro…