We study the period-doubling bifurcations to chaos in a logistic map with a nonlinearly modulated parameter and show that the bifurcation structure is modified significantly. Using the renormalisation method due to Derrida et al. we establish the universal behaviour of the system at the onset of chaos.
K. P. Harikrishnan and Dr. V . M. Nandakumaran, “Universal behaviour in a “modulated” logistic map”, Physics Letters A, vol. 125, pp. 465–468, 1987.