arXiv subjects

Ulises Chialva

Publications and source records attributed to Ulises Chialva.

3 recordsLinked to original sources

arXiv2026

Data-Based Dynamical Systems Reconstruction: An Adequacy/Reliability Test

In this work, we address the problem of validating the reconstruction of a stochastic system from noisy data. We demonstrate the limitations of criteria based solely on the loss function or on standard metrics used for reconstructing deterministic dynamics. We also propose an exploratory approach, based on a two-step test, which allows for a general assessment of the reconstruction without relying on arbitrary error-tolerance thresholds. However, we discuss how system degeneracy and non-identifiability, together with features intrinsic to stochastic dynamics, impose certain constraints on the application of this test.

math-ph↗

arXiv2022

Low-dimensional models of single neurons: A review

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as sub-threshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.

q-bio.NC↗

arXiv2019

On global mechanisms of synchronization in networks of coupled chaotic circuits and the role of the voltage-type coupling

A model for synchronization of coupled Nakano's chaotic circuits is studied. The Nakano circuit consists of a simple RLC circuit with a switch voltage-depending reset rule which generates a discontinuous dynamics. Thus, the model that we study is a network of identical spiking oscillators with integrate-and-fire dynamics. The coupling between oscillators is linear, but the network is subject to a common regime of reset depending on the global state of the oscillator population. This constitutes the simplest way of build pulse-coupled networks with arbitrary topology for this type of oscillators, and it allows the emergence of synchronous states and different reset regimes. The main result is that under certain hypothesis over the weight matrix (that represents the network topology) the different reset regimes match and the formalism of the master stability function can be generalized in order to study the stability of the synchronous state and the discontinuous dynamic of the network. Also, the low dimensionality of the Nakano's circuit allows to implement the saltation-matrix method and numerical simulations can be performed in order to analyze the role of the coupling mode in the synchronization regime of the network and the influence of the voltage-type variables.

nlin.AO↗