Some classes of models with lumped dynamics parameters of one-way population

The results of analysis of qualitative properties of some well-known and new dynamic models of one-way population with lumped parameters are viewed in the article. With the help of these models the influence of different factors on dynamics population is studied: nonlinear factors and acute conditions, the limiting number of population, different types of back-coupling, for example sharp decrease of population, the improvement of life quality, lagging factors and oscillatory dynamics of population. The article takes into consideration the lagging factors in dynamics models of population in a special case, when weight function has special view on basis of application of operation staff of fractional differentiation and integration. The possibility of allometry dynamics models of population on statistics is shown in the article.