I will briefly describe two bifurcation problems that arise (a) in discrete time model reference adaptive control and (b) in stabilizing infinite dimensional systems through truncations. In the first case noninvertible dynamics lead to new classes of instabilities and make the computation of basins of attraction difficult. In the second case, trying to relate open-loop to closed loop attractors via homotopy, give rise to broken (perturbed) transcritical bifurcations.

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