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We study the effects of coupling between layers of stochastic neural field models with laminar structure. In particular, we focus on how the propagation of waves of neural activity in each layer is affected by the coupling. Synaptic…
Similar activity patterns may arise from model neural networks with distinct coupling properties and individual unit dynamics. These similar patterns may, however, respond differently to parameter variations and, specifically, to tuning of…
In this paper, we study an excitable, biophysical system that supports wave propagation of nerve impulses. We consider a slow-fast, FitzHugh-Rinzel neuron model where only the membrane voltage interacts diffusively, giving rise to the…
We analyse the stochastic dynamics of a bistable system under the influence of time-delayed feedback. Assuming an asymmetric potential, we show the existence of a regime in which the systems dynamic displays excitability by calculating the…
Lateral inhibition resulting from a double-negative feedback loop underlies the assignment of different fates to cells in many developmental processes. Previous studies have shown that the presence of time delays in models of lateral…
We introduce a new numerical algorithm for solving the stochastic neural field equation (NFE) with delays. Using this algorithm we have obtained some numerical results which illustrate the effect of noise in the dynamical behaviour of…
Network couplings of oscillatory large-scale systems, such as the brain, have a space-time structure composed of connection strengths and signal transmission delays. We provide a theoretical framework, which allows treating the spatial…
Quantum transport in disordered systems poses intriguing fundamental questions about the interplay of disorder, interactions, and decoherence, with important implications for nanoscale energy transfer and quantum information transfer. Here,…
We analyze the stability of standing pulse solutions of a neural network integro-differential equation. The network consists of a coarse-grained layer of neurons synaptically connected by lateral inhibition with a non-saturating nonlinear…
We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays…
Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the…
This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with quadratic term and delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
We investigate the spatio-temporal dynamics of a ring cavity filled with a non-instantaneous Kerr medium and driven by a coherent injected beam. We show the existence of a stable mixed-mode solution that can be either extended or localized…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
Dislocation-assisted phase separation processes in binary systems subjected to irradiation effect are studied analytically and numerically. Irradiation is described by athermal atomic mixing in the form of ballistic flux with spatially…
Macroscopic oscillations of different brain regions show multiple phase relationships that are persistent across time and have been implicated routing information. Various cellular level mechanisms influence the network dynamics and…
We analyze the asymptotic stability of a nonlinear system of two differential equations with delay describing the dynamics of blood cell production. This process takes place in the bone marrow where stem cells differentiate throughout…