43 citations · 122 across the 13 of their papers we have counts for
13 papers
A dynamical system approach to modeling neural network activity in Drosophila orientation
S. Ismail, B. Ambrosio, M. A. Aziz-Alaoui +1
We introduce and analyze a class of neural network models motivated by the Drosophila central complex nervous system, designed to capture the emergence and dynamics of orientation-…
Consensus dynamics and coherence in hierarchical small-world networks
Yunhua Liao, Mohamed Maama, M. A. Aziz-Alaoui
The hierarchical small-world network is a real-world network. It models well the benefit transmission web of the pyramid selling in China and many other countries. In this paper, b…
Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event
K. Khalil, V. Lanza, D. Manceau +2
In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection-diffusion model, describing the spatio-temporal dynamics of a populat…
The generation of diverse traveling pulses and its solution scheme in an excitable slow-fast dynamics
Arnab Mondal, Argha Mondal, M. A. Aziz-Alaoui +3
In this paper, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatiall…
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…
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…
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…
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…
Fence-sitters Protect Cooperation in Complex Networks
Yichao Zhang, M. A. Aziz-Alaoui, Cyrille Bertelle +2
Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. In complex networks, because of the difficulty of formulating t…
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…
Effective Fokker-Planck Equation for Birhythmic Modified van der Pol Oscillator
R. Yamapi, G. Filatrella, M. A. Aziz-Alaoui +1
We present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Po…
Global stability analysis of birhythmicity in a self-sustained oscillator
R. Yamapi, G. Filatrella, M. A. Aziz-Aloui
We analyze global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit cycles variation of the van der Pol oscillato…