By Natali Hritonenko, Yuri Yatsenko (auth.)

Modern fiscal development is characterised by way of structural adjustments in accordance with the advent of latest applied sciences into economics. The alternative and renova­ tion of applied sciences in business environments present process technical swap is obviously one of many key points of monetary improvement. The mathematical modeling of evolutionary economics less than technical swap (TC) has been carefully thought of via many authors in the course of final a long time. there's a big choice of monetary methods and versions describing assorted points of technical swap. between those are the types of embodied technical development [19], [35], [70], [129], endogenous development versions [94], [102], the versions of technological concepts [31], [32], [41], and others. the viewpoint self­ association evolutionary technique is constructed in [20], [38], [122], [123], [124], [126], which unites the elements of diffusion of latest applied sciences, technological and behavioral range of organisations, studying mechanisms, age-dependent results, and different vital positive factors of real-life economics. normally, an curiosity in evolutionary economics has introduced massive growth within the description and conceptualization of the resources, features, course and results of technical switch [125]. despite the fact that, the modeling and regulate of know-how lifetime lower than technical swap has acquired particularly little consciousness in mathematical economics in con­ trary to different points of technical growth. The life of applied sciences has not often been officially handled as part of extra normal mathematical concept of monetary dynamics. an issue that's nonetheless to be resolved is composed in constructing the rational options of applied sciences' substitute lower than a variety of assumptions at the habit of technical change.

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The analysis of the asymptotic behavior of OP solutions provides an analogy of turnpike features for optimal trajectories, in particular, for technology lifetime. These features are simple to understand, though the mathematical treatment may become complicated. ' 3 INTEGRAL DYNAMICAL MODELS IN MATHEMATICAL ECOLOGY Present-day mathematical models of biological communities usually take into account aftereffect and joint influence of different exogenous and endogenous factors. Such models are based on various mathematical means, including integral equations.

If some part of output Yet) is supposed to be used for the purpose of development of the DS under consideration, then we obtain the models of evolving systems (see next Section). 5 = INTEGRAL MODELS OF EVOLVING SYSTEMS Let us consider some abstract (natural or artificial) evolving system (ES) consisting of separate system elements (SEs) which execute certain ES functions. Integral Dynamical Models in Control Theory 9 Suppose that the ES elements differ in accordance with their functions, the times of their creation, and the efficiency of function execution.

For analogous finitehorizon OP we show just less strong turn-pike properties (the turnpike theorems in normal and strong forms). The corresponding optimal distributions of EUs between production sectors are constructed and analyzed. We also study the case of different dynamics of the technological renovation in production sectors. For this purpose the same OP is considered in the generalization of two-sector model that includes two independent sought-for lifetimes al(t) and a2(t) of EUs for different sectors A and B (instead of one common control a(t) for the entire system).

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