Velocity-Amplitude relationship in the Gray-Scott autowave model in isolated conditions

Various chemical and biological systems involve autocatalytic steps and positive feedbacks which in spatial conditions can give them properties of active media, in particular autowave properties. The main autowave characteristics are velocity and amplitude. This report considers the autowave velocity-amplitude relation in the general mathematical model of active reactant formation from precursor with cubic kinetics followed by a linear inhibition/death step – the Gray-Scott model – in isolated conditions. The way to derive the explicit velocity-amplitude relation is proposed. This approach may be useful for investigation of more complex active media systems in biochemistry, combustion, and disease control. The work has been supported by the «RUDN University Program 5-100» and by the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-03-2020-223/3 (FSSF-2020-0018).