Дрейф, стабилизация и дестабилизация систем Патлака – Келлера – Cегеля с коротковолновым внешним сигналом

Abstract

In this article, we explore a community of two species placed on the inhomogeneous environment. We assume interspecific taxis as well as responding to the environmental fluctuations by tactic movement. We study the effect of the small-scale environmental fluctuations on the large-scale dynamics of the community following the line of Kapitza's theory of the upside-down pendulum. It turns out that, the only conductor of the effect of the fluctuations on the large-scale patterns is some drift of species. When the fluctuation takes the form of a travelling wave, there exist the quasi-equilibria, which are equilibria on average, roughly speaking. Examining the stability of the quasi-equilibria shows that, compared to the case of the homogeneous environment, increasing the magnitude of the fluctuations can destabilize the quasi-equilibria as well as stabilize them. It depends only on the speed at which the fluctuation wave prop-agates which of these effects occurs. Anyway, the effect is exponential in the amplitude of the wave.