Related papers: Pulsatile localized dynamics in delayed neural-fie…
Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity,…
In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate…
We consider the problem of the limit of bio-inspired spatially extended neuronal networks including an infinite number of neuronal types (space locations), with space-dependent propagation delays modeling neural fields. The propagation of…
We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…
Neural signals are characterized by rich temporal and spatiotemporal dynamics that reflect the organization of cortical networks. Theoretical research has shown how neural networks can operate at different dynamic ranges that correspond to…
Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical…
In spatially distributed cellular systems, it is often convenient to represent complicated auxiliary pathways and spatial transport by time-delayed reaction rates. Furthermore, many of the reactants appear in low numbers necessitating a…
Time lags are ubiquitous in biophysiological processes and more generally in real-world complex networks. It has been recently proposed to use information-theoretic tools such as transfer entropy to detect and estimate a possible delay in…
Randomly connected networks of excitatory and inhibitory spiking neurons provide a parsimonious model of neural variability, but are notoriously unreliable for performing computations. We show that this difficulty is overcome by…
We report a noise induced delay of bifurcation in a simple pulse-coupled neural circuit. We study the behavior of two neural oscillators, each individually governed by saddle-node dynamics, with reciprocal excitatory synaptic connections.…
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quantify the effect of delay through the buffering in the…
Network remodeling, or adaptation, in the presence of periodically driven forcings has hereto remained largely unexplored, despite the fact that a broad class of biological transport networks, e.g. animal vasculature, depends on periodic…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
We obtain a result on the behavior of the solutions of a general nonautonomous Hopfield neural network model with delay, assuming some general bound for the product of consecutive terms in the sequence of neuron charging times and some…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Spatiotemporal localized and extended structures associated with a subcritical finite wavenumber Hopf bifurcation are studied in the Purwins model (a three-variable FitzHugh-Nagumo version). Steady and time-dependent numerical continuation…
We have found a way for penetrating the space of the dynamical systems towards systems of arbitrary dimension exhibiting the nonlinear mixing of a large number of oscillation modes through which extraordinarily complex time evolutions…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
The Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the…