Quasi-fractal models of system sustainability

To study systems sustainability property quasi-fractal models are used: a system model and a system linkage model, and the concept of a sustainable kernel of a quasi-fractal system S is introduced. Within the framework of the Zermelo-Fraenkel system of axioms, the existence of the sustainability kernel of the system S and the kernel of sustainability of the system of connections of the system S is proved. For a numerical assessment of the sustainability of the system S and regulation of the sustainability property, it is proposed to use the digitalization function of closed formulas of the first-order language with equality of the signature Ω = 〈{f₁, …, f_n | n < ℵ₀},{P₁, …, P_m | m< ℵ₀},=〉, where f_i,i < n, is a n_i - ary function, P_j,j < m, is a m_j - ary predicate, [1]. The work uses modeling methods based on the algebraic formalization of systems.