Analytical investigation of the onset of bifurcation cascade in two logistic-like maps

Two modifications of the classical one-dimensional logistic map are proposed, which permitted analytical study of the onset of the bifurcation (period doubling) cascade. The modified maps are two-parametric ones. This introduces new features in their behaviour and makes them more flexible. The results can prove to be useful in the ecological (population dynamics) modeling, where the logistic map is a basic model and also in other fields of application.