  We identify a new mechanism for propagation into unstable states in spatially
extended systems, that is based on resonant interaction in the leading edge of
invasion fronts. Such resonant invasion speeds can be determined solely based
on the complex linear dispersion relation at the unstable equilibrium, but rely
on the presence of a nonlinear term that facilitates the resonant coupling. We
prove that these resonant speeds give the correct invasion speed in a simple
example, we show that fronts with speeds slower than the resonant speed are
unstable, and corroborate our speed criterion numerically in a variety of model
equations, including a nonlocal scalar neural field model.
