Mathematical models of single population

Mathematical models of single populations on an unlimited trophic resource, located on the line, or occupying the interconnected habitats are considered in this article. To describe the population in the first case the evolution equation is used, the system of ordinary differential equations is used in the second case. Problems for the generalized logistic population and population Ollie are solved. The solution of the static equation on a bounded interval is represented in quadratures for different boundary conditions. Conditions of possible existence of periodic solutions on the infinite line for population Ollie are found. The stability of homogeneous states is investigated. Conditions under which the trivial solution can be stable are obtained. Possibility of the existence several stable stationary points for the two-chamber model for the population Ollie is demonstrated.