From trigger to phase waves and back again

Transitions between trigger and phase waves are studied using a reaction–diffusion model, which admits both types of travelling wave activity. It is demonstrated that the transition from trigger waves to phase waves is preceded by qualitative changes in the dispersion relation of the former. These changes in dispersion in turn are provided by modified decay properties behind a solitary pulse. At high values of excitability the dispersion curve of trigger waves is destroyed upon a transcritical collision with the dispersion curve of phase waves, so both types of waves turn out to be connected in the small-wavelength region. As an important part of the study we present the results on the linear stability analysis of the waves close to the transition threshold. In particular, the stability of trigger waves with wiggly dispersion is thoroughly scrutinized and the stability of phase waves close to the transcritical collision is analyzed as well. We accompany our studies with one-dimensional simulations of the transition between phase and trigger waves under variation of the control parameter.