In this paper, we consider propagation direction, which can be used to
predict which species will occupy the habitat or win the competition
eventually, of bistable wave for a 3-species time-periodic lattice
competition system with bistable nonlinearity, aiming to address an open
problem proposed in [J.-S. Guo et al, The sign of traveling wave speed
in bistable dynamics, Discret. Contin. Dyn. Syst., 40 (2020),
3451]. As a first step, by transforming the competition system to a
cooperative one, we study the asymptotic behavior for the bistable wave
profile and then prove the uniqueness of the bistable wave speed.
Secondly, we utilize comparison principle and build up two couples of
upper and lower solutions to judge the sign of the bistable wave speed
which provides partially the answer to the open problem. As an
application, we reduce the time-periodic system to a space-time
homogeneous system, we obtain the corresponding criteria and carry out
numerical simulations to illustrate the availability of our results.
Moreover, an interesting phenomenon we found is that the two weak
competitors can wipe out the strong competitor under some circumstances.