In this paper recent work on the dynamics of lattice differential equations is surveyed. In
particular, results on propagation failure and lattice induced anisotropy for traveling wave or …

In this paper, we study the existence and stability of traveling waves in lattice dynamical
systems, in particular, in lattice ordinary differential equations (lattice ODEs) and in coupled …

We consider a one-dimensional lattice with diffusive nearest neighbor interaction, a
dissipative nonlinear reaction term and additive independent white noise at each node. We …

We obtain existence of traveling wave solutions for a class of spatially discrete systems,
namely, lattice differential equations. Uniqueness of the wave speed c, and uniqueness of …

We study the asymptotic behavior of solutions for lattice dynamical systems. We first prove
asymptotic compactness and then establish the existence of global attractors. The upper …

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 …

We consider infinite systems of ODEs on the two-dimensional integer lattice, given by a
bistable scalar ODE at each point, with a nearest neighbor coupling between lattice points …

The biologist JBS Haldane, when asked what we can learn about the Creator by examining
the world, is said to have replied “an inordinate fondness for beetles”[705]. Today's …

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 …