We study the existence of traveling waves in a one-dimensional network of integrate-and-#re neurons with #nite support coupling. We show that when the reset after spiking is su2ciently low, the interspike intervals (ISIs) for a traveling wave with an explicit #rst wave front can be computed. Further, we analytically derive a self-consistency equation that generates an explicit dispersion relati...

Integrated photonics is an emerging technology for many existing and future telecommunication data communication applications. One platform of particular interest silicon nitride (SiN), thanks to—among others—its very low-loss waveguides. However, it lacks active devices, such as lasers, amplifiers, photodiodes. For this, hybrid or heterogeneous integration needed. Here, we bring high-speed uni...

This paper is concerned with Nicholson’s blowflies equation, a kind of time-delayed reaction-diffusion equation. It is known that when the ratio of birth rate coefficient and death rate coefficient satisfies 1 < p d ≤ e, the equation is monotone and possesses monotone traveling wavefronts, which have been intensively studied in previous research. However, when p d > e, the equation losses its m...

We study multiplicity of the supercritical traveling front solutions for scalar reaction-diffusion equations in infinite cylinders which invade a linearly unstable equilibrium. These equations are known to possess traveling wave solutions connecting an unstable equilibrium to the closest stable equilibrium for all speeds exceeding a critical value. We show that these are, in fact, the only trav...

Many models in biology and ecology can be described by reaction-diffusion equations wit time delay. One of important solutions for these type of equations is the traveling wave solution that shows the phenomenon of wave propagation. The existence of traveling wave fronts has been proved for large class of equations, in particular, the monotone systems, such as the cooperative systems and some c...

This paper is concerned with the existence of the traveling bands to the Keller-Segel model with cell population growth in the form of a chemical uptake kinetics. We find that when the cell growth is considered, the profile of traveling bands, the minimum wave speed and the range of the chemical consumption rate for the existence of traveling wave solutions will change. Our results reveal that ...

This article concerns the asymptotic speed of spreading in a delay lattice differential equation without quasimonotonicity. We obtain the speed of spreading by constructing an auxiliary undelayed equation, whose speed of spreading is the same as that of the original equation. The minimal wave speed of bounded positive traveling wave solutions is obtained from the asymptotic spreading.