Modeling and Optimization of the Lifetime of Technologies

1. Front Matter

   Pages i-xxxvi

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2. Integral Dynamical Models of Evolving Systems

   1. Front Matter

      Pages 1-1

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   2. Integral Dynamical Models in Control Theory

      • Natali Hritonenko, Yuri Yatsenko

      Pages 3-12

   3. Integral Dynamical Models of Economic Systems

      • Natali Hritonenko, Yuri Yatsenko

      Pages 13-26

   4. Integral Dynamical Models in Mathematical Ecology

      • Natali Hritonenko, Yuri Yatsenko

      Pages 27-34

3. Analysis of One-Sector Integral Dynamical Models

   1. Front Matter

      Pages 35-35

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   2. Basic Optimization Problem in One-Sector Model

      • Natali Hritonenko, Yuri Yatsenko

      Pages 37-52

   3. Asymptotical Behavior of Optimal Trajectories and Turnpike Theorems

      • Natali Hritonenko, Yuri Yatsenko

      Pages 53-74

   4. Other Optimization Problems in One-Sector Models

      • Natali Hritonenko, Yuri Yatsenko

      Pages 75-100

4. Analysis of Multi-Sector Integral Dynamical Models

   1. Front Matter

      Pages 101-101

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   2. The Volterra Integral Equations with Sought-For Lower Limits of Integration

      • Natali Hritonenko, Yuri Yatsenko

      Pages 103-114

   3. Optimization in Two-Sector Models

      • Natali Hritonenko, Yuri Yatsenko

      Pages 115-134

   4. Optimization of Industry Conversion Rates

      • Natali Hritonenko, Yuri Yatsenko

      Pages 135-148

   5. Optimization in Three-Sector Model with Endogenous Technical Change

      • Natali Hritonenko, Yuri Yatsenko

      Pages 149-162

   6. Optimization in Multi-Sector Models

      • Natali Hritonenko, Yuri Yatsenko

      Pages 163-180

   7. Optimization of Technological Renovation in Hierarhical Ecological-Economic System

      • Natali Hritonenko, Yuri Yatsenko

      Pages 181-192

5. Applied Problems of Integral Dynamic Models

   1. Front Matter

      Pages 193-193

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   2. Numerical Algorithms for Integral Dynamical Models

      • Natali Hritonenko, Yuri Yatsenko

      Pages 195-214

   3. Application of Integral Models to Optimization of Technological Renovation

      • Natali Hritonenko, Yuri Yatsenko

      Pages 215-226

   4. Open Problems and Perspectives of Integral Models

      • Natali Hritonenko, Yuri Yatsenko

      Pages 227-232

Modern economic 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 [19], [35], [70], [129], endogenous growth models [94], [102], the models of technological innovations [31], [32], [41], and others. The perspective self­ organization evolutionary approach is developed in [20], [38], [122], [123], [124], [126], 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 [125]. 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.

• algorithms
• calculus
• economic dynamics
• economic system
• economics
• evolutionary economics
• integral equation
• integration
• Mathematica
• mathematical economics
• mathematical modeling
• model
• modeling
• optimization
• strategy

• Department of Cybernetics, Kiev University, Kiev, Ukraine

  Natali Hritonenko

• Glushkov Institute of Cybernetics, Ukrainian Academy of Sciences, Kiev, Ukraine

  Yuri Yatsenko

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