RODRIGUES , Serafim

The present work develops a new approach to studying parabolic bursting, and also proposes a novel four-dimensional canonical and polynomial-based parabolic burster. In addition to this new polynomial system, we also con- sider the conductance-based model of the Aplysia R15 neuron known as Plant's model, and a reduction of this prototypical...

Bursting is one of the fundamental rhythms that excitable cells can generate either in response to incoming stimuli or intrinsically. It has been a topic of intense research in computational biology for several decades. The classification of bursting oscillations in excitable systems has been the subject of active research since the early 1980s...

Abstract Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons driven by spike-timing-dependent plasticity (STDP) and temporal networks subject to homeostatic...

We study a class of planar integrate and fire (IF) models called adaptive integrate and fire (AIF) models, which possesses an adaptation variable on top of membrane potential, and whose subthreshold dynamics is piecewise linear (PWL). These AIF models therefore have two reset conditions, which enable bursting dynamics to emerge for suitable...

Neuronal excitability manifests itself through a number of key markers of the dynamics and it allows to classify neurons into different groups with identifiable voltage responses to input currents. In particular, two main types of excitability can be defined based on experimental observations, and their underlying mathematical models can be...

In this article, we present a computational study of the Conductance-Based Adaptive Exponential (CAdEx) integrate-and-fire neuronal model, focusing on its multiple timescale nature, and on how it shapes its main dynamical regimes. In particular, we show that the spiking and so-called delayed bursting regimes of the model are triggered by...

In this article, we present a computational study of the Conductance-Based Adaptive Exponential (CAdEx) integrate-and-fire neuronal model, focusing on its multiple timescale nature, and on how it shapes its main dynamical regimes. In particular, we show that the spiking and so-called delayed bursting regimes of the model are triggered by...

Neuronal excitability manifests itself through a number of key markers of the dynamics and it allows to classify neurons into different groups with identifiable voltage responses to input currents. In particular, two main types of excitability can be defined based on experimental observations, and their underlying mathematical models can be...

We propose a generalization of the neurotransmitter release model proposed in \emph{Rodrigues et al. (PNAS, 2016)}. We increase the complexity of the underlying slow-fast system by considering a degree-four polynomial as parametrization of the critical manifold. We focus on the possible transient and asymptotic dynamics, exploiting the...

In this article, we present a computational study of the Conductance-Based Adaptive Exponential (CAdEx) integrate-and-fire neuronal model, focusing on its multiple timescale nature, and on how it shapes its main dynamical regimes. In particular, we show that the spiking and so-called delayed bursting regimes of the model are triggered by...

We consider the chemostat model with the substrate concentration as the single measurement. We propose a control strategy that drives the system at a steady state maximizing the gas production without the knowledge of the specific growth rate. Our approach separates the extremum seeking problem from the feedback control problem such that each...

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how to use a continuation method to reconstruct the whole graph of the growth function. Two variants, in continuous and discrete time, are...

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how to use a continuation method to reconstruct the whole graph of the growth function. Two variants, in continuous and discrete time, are...