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The aim of the paper is to address the long time behavior of the Kuramoto model of mean-field coupled phase rotators, subject to white noise and quenched frequencies. We analyse the influence of the fluctuations of both thermal noise and…
One of the major challenges for long range, high speed Free-Space Optical (FSO) communication is turbulence induced beam wander. Beam wander causes fluctuations in the received intensity as well as crosstalk in mode division multiplexed…
We consider the theoretical constraints on interactions between coupled cortical columns. Each column comprises a set of neural populations, where each population is modelled as a neural mass. The existence of semi-stable states within a…
This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically…
Major Depressive Disorder (MDD) is a highly prevalent mental health condition, and a deeper understanding of its neurocognitive foundations is essential for identifying how core functions such as emotional and self-referential processing…
Spatiotemporal disorder has been recently associated to the occurrence of anomalous nonergodic diffusion of molecular components in biological systems, but the underlying microscopic mechanism is still unclear. We introduce a model in which…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
Critical dynamics of cortical neurons have been intensively studied over the past decade. Neuronal avalanches provide the main experimental as well as theoretical tools to consider criticality in such systems. Experimental studies show that…
We investigate Turing pattern formation in a stochastic and spatially discretized version of a reaction diffusion advection (RDA) equation, which was previously introduced to model synaptogenesis in \textit{C. elegans}. The model describes…
The temporal property of the compressible magneto-hydrodynamic (MHD) turbulence remains a fundamental unsolved question. Recent studies based on the spatial-temporal analysis in the global frame of reference suggest that the majority of…
We investigate the modes of oscillation of heterogeneous ring-networks of quadratic integrate-and-fire neurons with non-local, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient…
We study the random processes with non-local memory and obtain new solutions of the Mori-Zwanzig equation describing non-markovian systems. We analyze the system dynamics depending on the amplitudes $\nu$ and $\mu_0$ of the local and…
Temporal-lobe epilepsy in humans is often associated with widespread, synchronized neuron firing that co-occurs with traveling waves in local field potential. These traveling waves generate stochastic oscillations in a time series of…
Using an exactly solvable cortical model of a neuronal network, we show that, by increasing the intensity of shot noise (flow of random spikes bombarding neurons), the network undergoes first- and second-order non-equilibrium phase…
Representational drift refers to over-time changes in neural activation accompanied by a stable task performance. Despite being observed in the brain and in artificial networks, the mechanisms of drift and its implications are not fully…
Diffusion processes are studied theoretically for the case where the diffusion coefficient is itself a time and position dependent random function. We investigate how inhomogeneities and fluctuations of the diffusion coefficient affect the…
Understanding how neural dynamics shape cognitive experiences remains a central challenge in neuroscience and psychiatry. Here, we present a novel framework leveraging state-to-output controllability from dynamical systems theory to model…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
In this paper we present a general framework in which to rigorously study the effect of spatio-temporal noise on traveling waves and stationary patterns. In particular the framework can incorporate versions of the stochastic neural field…
In this paper, we study the dynamic formation of transients when plane waves impinge on a dispersive slab that abruptly changes its electrical properties in time. The time-varying slab alternates between air and metal-like states, whose…