We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map.
K. P. Harikrishnan and Dr. V . M. Nandakumaran, “Bifurcation structure and Lyapunov exponents of a modulated logistic map”, Pramana, vol. 29, pp. 533–542, 1987.