[1] **viXra:1103.0085 [pdf]**
*replaced on 2015-02-10 01:11:05*

**Authors:** Sergey V. Ershkov

**Comments:** 6 pages; Keywords: Logistic equation; Human population; reactive environment; Abel ODE

A key points of new approach for modeling of the population dynamics in reactive environment are presented here: 1) generalization of the Logistic equation to the case of reactive environment for modeling of population dynamics (or for the fulfilling of the ecological niches); 2) new type of asymptotic solution for such equation (which is tested on human population growth); 3) reduction to the Abel ODE in general case.
Due to a very special character of Abel ODE, it's general solution is proved to have a jumping or the break-down of the components for such a solution.
It means an existence of continuous general solution only at some definite, restricted range of time-parameter, or a possibility of sudden gradient catastrophe in regard to the components of solution (population growth), at the definite moment of time-parameter.

**Category:** Quantitative Biology