### Logistic Equation of Population Growth or Exhaustion of Main Resources: Generalization to the Case of Reactive Environment, Reduction to Abel Ode, Asymptotic Solution for Final Human Population Prognosis

**Authors:** Sergey V. Ershkov

**Comments:** 7 Pages. Keywords: Logistic equation; evolution of population; prognosis of Human population; reactive environment; catastrophes theory; Abel ODE

Here are presented a key points of new universal model for evolution of population in reactive environment: 1) generalization of the Logistic equation to the case of reactive environment for models of population dynamics in biology (also, for the model of exhaustion of main resources in geology, or for filling of an ecological niches in ecology, or for modeling of the capacities of a proper markets in economics), 2) new type of asymptotic solution for such equation (which is tested on human population growth), 3) reduction of such an equation to Abel ODE in general case.

**Category:** Quantitative Biology