Nonlinear waves with negative phase velocity.

Recently, waves propagating with negative phase velocity [simply called antiwaves (AWs)] have attracted great attention in the area of nonlinear oscillatory systems. In the present work we investigate the parameter conditions for AWs. So far AWs have been revealed from systems slightly beyond Hopf bifurcation or some other instabilities, and from some wave sources with certain restricted frequencies. Here we study general oscillatory media (including generalized complex Ginzburg-Landau systems and Brusselator model) and specify the parameter conditions of AWs by certain characteristic behaviors of the dispersion relation of the systems. Moreover, we predict that AWs and NWs (normal waves with positive phase velocity) can be realized at a same intrinsic parameter values but different pacing frequencies in parameter regions where the dispersion relation exhibits a maximum or minimum. All numerical simulations are perfectly consistent with these theoretical predictions where the oscillatory systems are driven by external periodic pacings with 1:1 frequency locking responses.