The theory of asymptotic speeds of spread and monotone traveling waves is established for
a class of monotone discrete and continuous‐time semiflows and is applied to a functional …

This paper deals with the limiting behavior of invariant measures of the stochastic delay
lattice systems. Under certain conditions, we first show the existence of invariant measures …

The current paper is devoted to the study of spatial spreading dynamics of monostable
equations with nonlocal dispersal in spatially periodic habitats. In particular, the existence …

We study the asymptotic behavior of solutions to a class of non-autonomous stochastic
lattice systems driven by multiplicative white noise. We prove the existence and uniqueness …

The periodic measures of the stochastic delay reaction-diffusion lattice systems are
investigated. Under a general condition, we prove the existence of periodic measures when …

Equations for a material that can exist stably in one of two homogeneous states are derived
from a microscopic or lattice viewpoint with the assumption that the evolution follows a …

We study traveling waves of a discrete system where f and g are Lipschitz continuous with g
increasing and f monostable, ie, f (0)= f (1)= 0 and f> 0 on (0, 1). We show that there is a …

The dynamics of infinite-dimensional lattice systems is studied. A necessary and sufficient
condition for asymptotic compactness of lattice dynamical systems is introduced. It is shown …

This paper is concerned with the dynamics of the stochastic reaction–diffusion lattice
systems defined on the entire integer set driven by locally Lipschitz nonlinear noise. We …

In this paper, we study the existence, uniqueness and asymptotic stability of travelling
wavefronts of the following equation: where x∈ R, t> 0, D, d> 0, r⩾ 0, b∈ C1 (R) and b (0) …