We study resource matching – the relationship between resource supply and forager numbers – under conditions of fluctuating population dynamics in a two-patch system. For the inter-patch dispersal we apply the patch-departure rule following the principle of the ideal free distribution: leave the current patch of residence if local conditions are worse than conditions elsewhere on average. We show that such a dispersal rule synchronises cyclic and chaotic local population dynamics, but unlike many other dispersal rules, leaves the underlying population dynamics untouched. We also show that the IFD dispersal rule is not very sensitive to biased information and navigation failures during the dispersal phase. Even under such circumstances we observe a quick process of populations becoming synchronised, even when the population dynamics are chaotic. We conclude that an IFD patch-departure rule represents an ESS dispersal behaviour towards which the dispersal patterns should evolve.