Models of spatial and temporal dynamics of trophic communities are considered and numerically investigated. Stability of equilibriums of two trophic levels models is analytically studied. Active migrations are described on the bases of idea that acceleration of directed migration of predators is pro-rate the density gradient of prey populations. High migration activity of predators ensures the stability of complex non-uniform spatial regimes even when the abundance of predators is constant. In this case both summarized consumption of preys by predators and total number of preys considerably exceed equilibrium meanings of homogeneous regime, that takes place when predators are not able to migrate directionally. In three levels trophic system plant resource-pest-predator the increase in migration activity of predator leads to the increase of its abundance and the abundance of pest while the biomass of the resource decreases. This result is interpreted as an example of non-effective biological control when predators with high searching ability are used.