  We consider the properties of a slow-fast prey-predator system in time and
space. We first argue that the simplicity of prey-predator system is apparent
rather than real and there are still many of its hidden properties that have
been poorly studied or overlooked altogether. We further focus on the case
where, in the slow-fast system, the prey growth is affected by a weak Allee
effect. We first consider this system in the non-spatial case and make its
comprehensive study using a variety of mathematical techniques. In particular,
we show that the interplay between the Allee effect and the existence of
multiple timescales may lead to a regime shift where small-amplitude
oscillations in the population abundances abruptly change to large-amplitude
oscillations. We then consider the spatially explicit slow-fast prey-predator
system and reveal the effect of different time scales on the pattern formation.
We show that a decrease in the timescale ratio may lead to another regime shift
where the spatiotemporal pattern becomes spatially correlated leading to
large-amplitude oscillations in spatially average population densities and
potential species extinction.
