Abstract It is possible for a nonlinear dissipative system (the follower) to have a trajectory in phase space synchronized to that of another identical system (the driver) by means of coupling to the former rom the latter. This synchronization can remain unaffected in the presence of so-called neutral feedback (coupling from the follower back to the driver such that the synchronized trajectories are unchanged). If the strength of the neutral feedback exceeds a critical size, there is a bifurcation and the synchronized trajectories become unstable. In the immediate vicinity of this critical strength, there can be complete uncertainly, for given initialsconditions, as to whether or not synchronization occurs. Any two neighboring sets of initial conditions, no matter how close, may lead to differing results. This is an example of what is called riddled behavior, and the bifurcation is precursive.