27 citations · 52 across the 13 of their papers we have counts for
13 papers
Physics-constrained inference of somatic dynamics from dendritic recordings with sparse somatic supervision in weakly coupled two-compartment neuron model
Abdeltif Oujbara, Benjamin Ambrosio, M. A. Aziz-Alaoui
Somatic membrane potential is the primary determinant of neuronal output, yet it remains inaccessible in many experimental setups where only dendritic recordings are available. Rec…
Non trivial dynamics in the FizHugh-Rinzel model and non-homogeneous oscillatory-excitable reaction-diffusions systems
B. Ambrosio, M. A. Aziz-Alaoui, Argha Mondal +3
In this article, we discuss the dynamics of the 3-dimensional FitzHugh-Rinzel (FHR) model and a class of non-homogeneous FitzHugh-Nagumo (Nh-FHN) Reaction-Diffusion systems. The Nh…
Periodically kicked feedforward chains of simple excitable FitzHugh-Nagumo neurons
B. Ambrosio, S. M. Mintchev
This article communicates results on regular depolarization cascades in periodically-kicked feedforward chains of excitable two-dimensional FitzHugh-Nagumo systems driven by suffic…
Beyond the brain: towards a mathematical modeling of emotions
B. Ambrosio
Emotions are a central key for understanding human beings and of fundamental importance regarding their impact in human and animal behaviors. They have been for a long time a subje…
On a coupled time-dependent SIR models fitting with New York and New-Jersey states COVID-19 data
Benjamin Ambrosio, M. A. Aziz-Alaoui
This article describes a simple Susceptible Infected Recovered (SIR) model fitting with COVID-19 data for the month of march 2020 in New York (NY) state. The model is a classical S…
Simulating brain rhythms using an ODE with stochastically varying coefficients
Benjamin Ambrosio, Lai-Sang Young
The brain produces rhythms in a variety of frequency bands. Some are likely by-products of neuronal processes; others are thought to be top-down. Produced entirely naturally, these…
Emergent Properties in a V1-Inspired Network of Hodgkin-Huxley Neurons
M. Maama, B. Ambrosio, M. A. Aziz-Alaoui +1
This article is devoted to the theoretical and numerical analysis of a network of excitatory and inhibitory neurons of Hodgkin-Huxley (HH) type, for which the topology is inspired…
Qualitative Analysis of certain Reaction-Diffusion Systems of the FitzHugh-Nagumo type
Benjamin Ambrosio
This article aims to provide insights into the qualitative analysis of some nonlinear Reaction-Diffusion (RD) systems arising in Neuroscience. We first introduce a non-homogeneous…
Canard Phenomenon in a modified Slow-Fast Leslie-Gower and Holling type scheme model
B. Ambrosio, M. A. Aziz-Alaoui, R. Yafia
Geometrical Singular Perturbation Theory has been successful to investigate a broad range of biological problems with different time scales. The aim of this paper is to apply this…
Propagation of bursting oscillations in coupled Hodgkin-Huxley Reaction-Diffusion systems
B. Ambrosio, M. A. Aziz-Alaoui, A. Balti
We consider networks of reaction-diffusion systems of Hodgkin-Huxley type. We give a general mathematical framework, in which we prove existence and unicity of solutions as well as…
Hopf Bifurcation in an Oscillatory-Excitatory Reaction-Diffusion Model with Spatial heterogeneity
B. Ambrosio
We focus on the qualitative analysis of a reaction-diffusion with spatial heterogeneity. The system is a generalization of the well known FitzHugh-Nagumo system in which the excita…
Attractor and synchronization for a complex network of reaction-diffusion systems of FitzHugh-Nagumo type
B. Ambrosio, M. A. Aziz-Alaoui, V. L. E. Phan
We focus on the long time behavior of complex networks of reaction-diffusion (RD) systems. We prove the existence of the global attractor and a -bound for a network of…
Weakly coupled two slow- two fast systems, folded node and mixed mode oscillationsM
M. Krupa, B. Ambrosio, M. A. Aziz-Alaoui
We study Mixed Mode Oscillations (MMOs) in systems of two weakly coupled slow/fast oscillators. We focus on the existence and properties of a folded singularity called FSN II that…