  The basic model of purposeful kinesis was developed recently (Gorban and
Cabukoglu, Ecol. Complex. 2018, 33, 75 83) on the basis of the let well enough
alone idea. According to this model the diffusion drops while the reproduction
coefficient is increasing. That is, species prefer to stay in a good condition
and the population gives birth; otherwise, in the bad situation individuals
want to run away because of the fatal conditions. In this study, we analyse the
impact of the purposeful kinesis model on running waves. The running waves in
the population with kinesis are studied using numerical experiments. Both
monotonic and non monotonic (Allee effect) dependence of the reproduction
coefficient on the population density are studied. The possible benefits of the
purposeful kinesis are demonstrated: with the higher diffusion, while the
population without kinesis ends up with extinction, the population with kinesis
stays alive and has the running wave behavior. While the kinesis of the prey
population is decreasing, the wave amplitude gets smaller. On the other hand,
for the lower kinesis of predators they have a sharp increase.
