For a class of 1-dimensional lattice dynamical systems we prove the existence of periodic traveling waves with prescribed speed and arbitrary period. Then we study asymptotic behaviour of such waves for big values of period and show that they converge, in an appropriate topology, to a solitary traveling wave.

This paper is concerned with the traveling wavefronts of Belousov-Zhabotinskii model with time delay. By constructing upper and lower solutions and applying the theory of asymptotic spreading, the minimal wave speed is obtained under the weaker condition than that in the known results. Moreover, the strict monotonicity of any monotone traveling wavefronts is also established.

This paper is concerned with a lattice dynamical system modeling the evolution of susceptible and infective individuals at discrete niches. We prove the existence of traveling waves connecting the disease-free state to non-trivial leftover concentrations. We also characterize the minimal speed of traveling waves and we prove the non-existence of waves with smaller speeds.

We study the traveling waves of reaction-diffusion equations for a diffusive SIR model. The existence of traveling waves is determined by the basic reproduction number of the corresponding ordinary differential equations and the minimal wave speed. Our proof is based on Schauder fixed point theorem and Laplace transform.

In this article, we study the existence of traveling wavefronts for integrodifference equation with a bilateral exponential kernel, namely, the Laplacian kernel. The existence of traveling wavefronts is proved by combining the monotone iteration technique with the upper and lower solution method. The minimal spreading speed c∗ is given, which can be figured out exactly when all parameters are g...

This note is devoted to the study on the traveling wavefronts to the Nicholson’s blowflies equation with diffusion, a time-delayed reaction-diffusion equation. For the critical speed of traveling waves, we give a detailed analysis on its location and asymptotic behavior with respect to the mature age.

We prove that if a solution of an equation of KdV type is bounded above by a traveling wave with an amplitude that decays faster than a given linear exponential then it must be zero. We assume no restrictions neither on the size nor in the direction of the speed of the traveling wave.

This paper is concerned with traveling wavefronts in a LotkaVolterra model with nonlocal delays for two cooperative species. By using comparison principle, some existence and nonexistence results are obtained. If the wave speed is larger than a threshold which can be formulated in terms of basic parameters, we prove the asymptotic stability of traveling wavefronts by the spectral analysis metho...

Transportation network improvements are commonly evaluated by estimating average speeds from atransportation/traffic model and converting them into emission estimates using an environmental model such asMOBILE or EMFAC. Unfortunately, recent research has demonstrated that average speed, and perhaps evensimple estimates of the amount of delay and the number of vehicle stops on a ...

A class of integral recursion models for the growth and spread of a synchronized single-species population is studied. It is well known that if there is no overcompensation in the fecundity function, the recursion has an asymptotic spreading speed c*, and that this speed can be characterized as the speed of the slowest non-constant traveling wave solution. A class of integral recursions with ov...