Correlation between models of population dynamics in continuous and discrete time

There exist two main problems in the analysis of correlation between population dynamics models with a discrete and continuous time space, which we consider at present paper. One problem is finding the discrete analog of the well-known Verhulst model. The other is the reason of appearance of chaotic regimes and oscillations with big periods in Moran-Rickerʹs models. Also we consider the new one-dimensional models with different assumptions about birth and death processes in populations.