  We consider a discrete version of reaction-diffusion equations. A typical
example is the fully overdamped Frenkel-Kontorova model, where the velocity is
proportional to the force. We also introduce an additional exterior force
denoted by $\sigma$. For general discrete and fully nonlinear dynamics, we
study traveling waves of velocity $c=c(\sigma)$ depending on the parameter
$\sigma$. Under certain assumptions, we show properties of the velocity diagram
$c(\sigma)$ for $\sigma\in [\sigma^-,\sigma^+]$. We show that the velocity $c$
is nondecreasing in $\sigma \in (\sigma^-,\sigma^+)$ in the bistable regime,
with vertical branches $c\ge c^+$ for $\sigma=\sigma^+$ and $c\le c^-$ for
$\sigma=\sigma^-$ in the monostable regime.
