Related papers: Traveling Wave Solutions to a Neural Field Model W…
We rigorously prove the existence of traveling fronts in neural field models with lateral inhibition coupling types and smooth sigmoidal firing rates. With Heaviside firing rates as our base point (where unique traveling fronts exist), we…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
We prove a principle of linearized stability for traveling wave solutions to neural field equations posed on the real line. Additionally, we provide the existence of a finite dimensional invariant center manifold close to a traveling wave,…
In this paper, we study the traveling wave solutions to the density-suppressed motility model describing the ``self-trapping'' mechanism that induces spatio-temporal pattern formations observed in the experiment. We establish the existence…
We rigorously prove the existence and uniqueness of fast traveling pulse solutions to the singularly perturbed neural field system with linear feedback and Heaviside nonlinearity structure within a spatial convolution. Although a…
We study travelling wave solutions of a 1D continuum model for collective cell migration in which cells are characterised by position and polarity. Four different types of travelling wave solutions are identified which represent…
In 1992 G. B. Ermentrout and J. B. McLeod published a landmark study of traveling wave fronts for a differential-integral equation modeling a neural network. Since then a number of authors have extended the model by adding an additional…
The purpose of this work is to introduce a concept of traveling waves in the setting of periodic metric graphs. It is known that the nonlinear Schr{\"o}dinger (NLS) equation on periodic metric graphs can be reduced asymptotically on long…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
Neural field equations offer a continuous description of the dynamics of large populations of synaptically coupled neurons. This makes them a convenient tool to describe various neural processes, such as working memory, motion perception,…
We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…
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 spatially extended system is modelled using the nearest neighbor…
Spatiotemporal patterns such as traveling waves are frequently observed in recordings of neural activity. The mechanisms underlying the generation of such patterns are largely unknown. Previous studies have investigated the existence and…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…
In this paper we study the invasion fronts of spatially periodic monotone reaction-diffusion systems in a multi-dimensional setting. We study the pulsating traveling waves that connect the trivial equilibrium, for which all components of…
The present paper is concerned with the existence of traveling wave solutions of the asymptotic model, derived by the authors in a previous work, to approximate the unidirectional evolution of a collision-free plasma in a magnetic field.…
Traveling waves of neural activity emerge in cortical networks both spontaneously and in response to stimuli. The spatiotemporal structure of waves can indicate the information they encode and the physiological processes that sustain them.…
It has been reported that traveling waves propagate periodically and stably in sub-excitable systems driven by noise [Phys. Rev. Lett. \textbf{88}, 138301 (2002)]. As a further investigation, here we observe different types of traveling…
We study periodic travelling waves in the Theta model for a linear continuum of synaptically-interacting neurons. We prove that when the neurons are oscillatory, at least one periodic travelling of every wave number always exists. In the…