We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for the whole system, giving rise to a Parrondo's dynamic type paradox
Cima, A., Gasull, A., Mañosa, V. Parrondo's dynamic paradox for the stability of non-hyperbolic fixed points. "Discrete and continuous dynamical systems. Series A", Febrer 2018, vol. 38, núm. 2, p. 889-904.