Monotonicity, asymptotics and uniqueness of travelling wave solution of a non-local delayed lattice dynamical system

Abstract

A delayed lattice dynamical system with non-local diffusion and interaction is considered in this paper. The exact asymptotics of the wave profile at both wave tails is derived, and all the wave profiles are shown to be strictly increasing. Moreover, we prove that the wave profile with a given admissible speed is unique up to translation. These results generalize earlier monotonicity, asymptotics and uniqueness results in the literature.

Traveling waves for a lattice dynamical system arising in a diffusive endemic model

“…For monostable equations or monostable monotone systems, we refer to e.g. [6,7,8,15,16,21,23,25,29,30,34,35,38,41]. Waves for bistable lattice dynamical systems have been studied in e.g.…”

Spreading dynamics of a discrete Nicholson's blowflies equation with distributed delay

“…Besides, they are also natural outcomes of discretizing the corresponding spatial continuous model. In the literature, some discretizations of classical continuous models have been proposed, such as the discrete Fisher's equation [28], discrete Nagumo equation [27], discrete Allen-Cahn equation [3] and discrete Lotka-Volterra equation [7], etc., and there have been many studies focussed on the study of propagation dynamics of various types of discrete equations, see [4,9,10,14,[19][20][21][22][23][24][25][26] and the references therein. However, the approximation of continuous models by spatial discretization is a delicate issue, and it is well known that there could exist essential differences between a discrete model and its associated continuous version.…”

Global Stability of Non-monotone Noncritical Traveling Waves for a Discrete Diffusion Equation with a Convolution Type Nonlinearity

“…To the best of our knowledge, the existence of traveling waves and other properties, such as monotonicity and uniqueness of traveling waves of (1.5) were well studied. We refer the readers to [15,16] for bistable case, [1,7,14,25] for monotone monostable case, and [5,6,27,30] for nonmonotone monostable case. However, little has been done for the stability of traveling waves of (1.1) and (1.5), when the function g is not monotone.…”