The analytical solutions of the harvesting Verhulst’s evolution equation

The Verhulst differential equation is one of the evolutionary equations most widely known in ecology. Its analytical solution is applied to explain the growth dynamics of populations with limited resources. The situation when the harvesting or “influence” function, i.e. the additional term proportional to the population concentration, is controlled by the time-dependent coefficient is analyzed. Several examples when this equation has the analytical solutions whose dependence on the parameters is expressed in an explicit form are presented. The estimation of the influence function in real experiments with bread mold is presented. The stability and harvesting functions in the general case are discussed.