A Hopf bifurcation occurs at α = 0, where periodic oscillations with frequency ω are observed. We now couple two systems of the sort in (6), each with a potentially different frequency ω q , via linear migration terms with migration rate ν. To lowest order (not displaying cubic terms), the coupled system in cartesian coordinates iṡ x 1 = αx 1 − ω 1 y 1 − νx 1 + νx 2 y 1 = αy 1 + ω 1 x 1 − νy 1 + νy 2 x 2 = αx 2 − ω 2 y 2 − νx 2 + νx 1 y 2 = αy 2 + ω 2 x 2 − νy 2 + νy 1