The effect of variable migration rate on transference of dynamical regime from origin to destination in a simple metapopulation of two populations linked by unidirectional movement. In the top panel are cases where the origin population has cyclical dynamics and the destination has steady state dynamics when in isolation, while in the bottom panel the opposite is true. As the movement rate (δ; horizontal axis) increases, there is a phase-transition at which point the destination population's dynamics (indicated by the vertical axis) switch to match those of the origin. We fit a binomial spline to highlight this transition point. We see that even with very small rates of migration, a stable population can be converted to a cyclical one (top panel). Yet, it is more difficult to convert a cyclical population to one with steady state dynamics (bottom panel). Three parametrizations are recorded here (color; see legend), with additional parameter μ = 0.15 being the same for both populations. Finally, note that the two values of \(\tilde{R_0}\) listed in the legend correspond to the two populations, with the larger value corresponding to the steady state population and the smaller value the cyclical population (when in isolation) .