Model Development and OptimizationSpringer US, 30. apr. 1999 - 250 sider At present, concerning intensive development of computer hardware and software, computer-based methods for modeling of difficult problems have become the main technique for theoretical and applied investigations. Many unsolved tasks for evolutionary systems (ES) are an important class of such problems. ES relate to economic systems on the whole and separate branches and businesses, scientific and art centers, ecological systems, populations, separate species of animals and plants, human organisms, different subsystems of organisms, cells of animals and plants, and soon. Available methods for modeling of complex systems have received considerable attention and led to significant results. No large-scale programs are done without methods of modeling today. Power programs, health programs, cosmos investigations, economy designs, etc. are a few examples of such programs. Nevertheless, in connection with the permanent complication of contemporary problems, existing means are in need of subsequent renovation and perfection. In the monograph, along with analysis of contemporary means, new classes of mathematical models (MM) which can be used for modeling in the most difficult cases are proposed and justified. The main peculiarities of these MM offer possibilities for the description ofES; creation and restoration processes; dynamics of elimination or reservation of obsolete technology in ES; dynamics of resources distribution for fulfillment of internal and external functions ofES; and so on. The complexity of the problems allows us to refer to the theory and applications of these MM as the mathematical theory of development. For simplicity, the title "Model Development and Optimization" was adopted. |
Indhold
NATURAL ES | 7 |
GENERALIZED STRUCTURE OF TWO ES INTERACTIONS | 13 |
COMPARISON WITH WELLKNOWN MM | 20 |
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ai(t algorithm application approximate asymptotic bio-mass biosphere c₁ condition of Theorem control functions created decreasing determined differentiable distribution dose dynamic dynamic system economic elements error estimate example external functions external product external resources factor FCCP fi(t follows formulae geometrical progressions given Glushkov V.M. ill-posed problem immune Immunology indices of efficiency instant integral interaction internal investigation Ivanov V.V. Kiev labor functions Lemma Let us consider lymphocytes m-type m₁ mathematical models maximal means method metric space minimizing Nauka neo-sphere nonnegative norm obsolete WP obtained optimization problems organism P₁(t parameters photosynthesis plant prehistory problem C.1 proliferating proof properties qualitative quantity rate of creation relations respective round-off error Russian segment t^,T similar solution stimulated structure subsystem temporal theory total number unique unit usually values Volterra integral equations Ymin(t
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