Naimark–Sacker bifurcations in linearly coupled quadratic maps

We report exact analytical expressions locating the 0→1, 1→2 and 2→4 bifurcation curves for a prototypical system of two linearly coupled quadratic maps. Of interest is the precise location of the parameter sets where Naimark–Sacker bifurcations occur, starting from a non-diagonal period-2 orbit. This result is the key to understand the onset of synchronization in networks of quadratic maps.