Anna Tarasenko, Manuel González Hernández, Oleksandr Karelin
We continue on studying of systems whose state depends on time and whose resources are renewable based on functional operators with shift. In previous articles, we consider the term which describe results of reproductive processes as a linear expression or as a shift summand. In this work the reproductive term is represented with the help of an integral which contains a degenerate kernel. A cyclicmodel of evolution of the system with a renewable resource is developed, obtained equilibrium proportion is analyzed. We propose a method of solution of the balance equation, we determine an equilibrium state of the system. The inverse operator of equation and it approximations are constructed. In what follows, we program to use their forms to observe modifications of our system period by period. Having appliedthis model , we can investigate problems of nature systems and production.