  Including an extra reactant in the Gray-Scott reaction-diffusion model, the
dynamical competition between different chemical species during the Turing
pattern formation can lead to species territory invasion phenomenon among
different patterns of respective species. We report a peculiar oscillatory
change on respective mass of a 2D pattern under competition condition by
numerical simulation. The invaded Turing spot pattern can turn from a steady
fading mode into a spontaneous resonant oscillation mode, the firefly lighting
mode, which occurs synchronously among nearest neighboring spots, until the
largest spot is annihilated finally. Such resonant oscillation behavior for
annihilation can continue but in a more chaotic way towards final dying of the
pattern by invasion of another pattern. The resonant frequency is found to be
intrinsic character of the invaded pattern, depending on its control
parameters.
