Modeling and Optimization of the Lifetime of Technologies
growth is characterized by structural changes based on the introduction of new technologies into economics. The replacement
and renova- tion of technologies in industrial environments undergoing technical change is clearly one of the key aspects
of economic development. The mathematical modeling of evolutionary economics under technical change (TC) has been rigorously
considered by many authors during last decades. There is a wide variety of economic approaches and models describing different
aspects of technical change. Among these are the models of embodied technical progress , , , , endogenous
growth models , , the models of technological innovations , , , and others. The perspective self- organization
evolutionary approach is developed in , , , , , , which unites the aspects of diffusion of new
technologies, technological and behavioral diversity of firms, learning mechanisms, age-dependent effects, and other important
features of real-life economics. On the whole, an interest in evolutionary economics has brought considerable progress in
the description and conceptualization of the sources, characteristics, direction and effects of technical change . However,
the modeling and control of technology lifetime under technical change has received rather little attention in mathematical
economics in con- trary to other aspects of technical progress. The lifetime of technologies has rarely been formally treated
as a part of more general mathematical theory of economic dynamics. A problem which is still to be resolved consists in establishing
the rational strategies of technologies' replacement under various assumptions on the behavior of technical change.
Part I: Integral Dynamical Models of Evolving Systems. 1. Integral Dynamical Models in Control Theory. 2. Integral Dynamical
Models of Economic Systems. 3. Integral Dynamical Models in Mathematical Ecology. Part II: Analysis of One-Sector Integral
Dynamical Models. 4. Basic Optimization Problem in One-Sector Model. 5. Asymptotical Behavior of Optimal Trajectories and
Turnpike Theorems. 6. Other Optimization Problems in One-Sector Models. Part III: Analysis of Multi-Sector Integral Dynamical
Models. 7. The Volterra Integral Equations with Sought-for Lower Limits of Integration. 8. Optimization in Two-Sector Models.
9. Optimization of Industry Conversion Rates. 10. Optimization in Three-Sector Model with Endogenous Technical Change. 11.
Optimization in Multi-Sector Models. 12. Optimization of Technological Renovation in Hierarchical Ecological-Economic System.
Part IV: Applied Problems of Integral Dynamical Models. 13. Numerical Algorithms for Integral Dynamical Models. 14. Application
of Integral Models to Optimization of Technological Renovation. 15. Open Problems and Perspectives of Integral Models. References.
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