Study of the Equilibrium State of Systems withTwo Renewable Resources Based on FunctionalOperators with Shift

In previous works we proposed a method for thestudy of systems with one renewable resource. The separation of the individual and the group parameters and the discretization of time led us to scalar linear functional equations with shift. Cyclic models, in which the initial state of the system coincides with the final state, were considered. In this work, we present cyclic models for systems with two renewable resources. In modelling, the interactions and the reciprocal influencesbetween these two resources are taken into account. Analysis of the models is carried out in weighted Holder spaces. For the solution of the balance integral equation with degenerate kernels and inverse operators, a modified Fredholm method is proposed. The modified Fredholm method is applied to the analysis of balance equation. The equilibrium state of the system with renewable resources is found.