Category-functor modelling of natural systems

Cybernetics and Systems

Volumn 30, Issue 6, 1999, Pages 571-585

  Levich, A P ^a   Solov'yov A V ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

NATURAL SYSTEMS;

COMPUTER SYSTEMS PROGRAMMING;

EID: 0032674281     PISSN: 01969722     EISSN: 10876553     Source Type: Journal    
DOI: 10.1080/019697299125118     Document Type: Article

References (30)

1. Alexeyev, V. L. and A. P. Levich. 1997. A search for maximum species abundances in ecological communities under conditional diversity optimization. Bull. Math. Biol. 59:649-677.
2. Baianu, J. and M. Marinescu. 1968. Organismic supercategories. I. Proposals for a general unitary theory of systems. Bull. Math. Biophys. 30:625-635.
3. Baianu, J. 1970. Organismic supercategories. II. On multistable systems. Bull. Math. Biophys. 32:539-561.
4. Bartholomay, A. F. 1960. Molecular set theory. A mathematical representation for chemical reaction mechanisms. Bull. Math. Biophys. 22:285-307.
5. Bartholomay, A. F. 1965. Molecular set theory. II. An aspect of biomathematical theory of sets. Bull. Math. Biophys. 27:235-251.
6. Bourbaki, N. 1960. Elements de Mathématique. Théorie des ensembles. Paris: Hermann.
7. Bucur, I., and A. Deleanu. 1968. Introduction to the Theory of Categories and Functors. London: John Wiley.
8. Goldblatt, R. 1979. Topoi. The Categorial Analysis of Logic. Amsterdam: North-Holland.
9. Leguizamon, C. A. 1975. Concept of energy in biological systems. A theory for environmental systems. Bull. Math. Biol. 37:565-572, 675-689.
10. Leguizamon, C. A. 1993. The periodic continuous effect in terms of the algebraic rational theory. J. Biol. Systems 1:1-25.
11. Levich, A. P. 1978. Information as system structure. Semiotika i Informatika 10:116-132 (in Russian).
12. Levich, A. P. 1980. The Structure of Ecological Communities. Moscow: Moscow University in Russian.
13. Levich, A. P. 1982. Sets Theory, the Language of Category Theory and Their Applications in Theoretical Biology. Moscow: Moscow University (in Russian).
14. Levich, A. P., E. D. Liubimova, and G. Sh. Martashvili. 1986. Species structure and the consumption of substrate and energy factors in laboratory algo-coenosis. Ecological Forecasting, Moscow, pp. 69-103 (in Russian).
15. Levich, A. P., and N. G. Bulgakov. 1992. Regulation of species and size composition in phytoplankton communities in situ by N:P ratio. Russian Journal of Aquatic Ecology 2:149-159.
16. Levich, A. P., A. A. Khudoyan, N. G. Bulgakov, and V. A. Artiukhova 1992. On the possibility of species and size community structure control in experiments with natural phytoplankton in vitro. Biologicheskiye Nauki 7:17-29 in Russian.
17. Levich, A. P., V. L. Alekseev, and S. Yu. Rybakova. 1993. Optimization of the structure of ecological communities: Model analysis. Biophyzics 38:903-911.
18. Levich, A. P., and N. G. Bulgakov. 1993. About the possibility of controlling of algal community structure in lab. Biology Bulleting of the Russian Academy of Sciences 20:457-464.
19. Levich, A. P., D. G. Zamolodchikov, and S. Yu. Rybakova. 1993. A study of the adequacy of a category-theoretic model of phytoplankton communities. Ecological Monitoring and Modeling Problems in Ecology 15:234-246 (in Russian.
20. Levich, A. P., V. L. Alekseev, and V. A. Nikulin. 1994. Mathematical aspects of variational modeling in ecology of communities, Matematicheskoye Mod-elirovanie 6:55-76 (in Russian).
21. Levich, A. P., and V. L. Alexeyev. 1997. The entropy extremal principle in the ecology of communities: Results and discussion. Biophysics. 42:525-532.
22. Levich, A. P., V. N. Maximov, and N. G. Bulgakov. 1997. Theoretical and Experimental Ecology of Phytoplankton: The Structure and Function of Communities Control. Moscow: SAL Press (in Russian).
23. Lurie, D., J. Valls, and J. Vagensberg. 1983. Thermodynamic approach to biomass distribution in ecological systems. Bull. Math. Biol. 45:869-872.
24. Rashevsky, N. 1954. Topology and life. In search of general mathematical principles in biology and sociology. Bull. Math. Biophys. 16:317-348.
25. Rashevsky, N. 1955a. The geometrization in biology. Bull. Math. Biophys. 17:31-56.
26. Rashevsky, N. 1955b. Some remarks on topological biology. Bull. Math. Biophys. 17:207-218.
27. Rashevsky, N. 1955c. Life, information theory and topology. Bull. Math. Biophys. 17:229-235.
28. Rosen, R. 1958a. A relational theory of biological systems. Bull. Math. Biophys. 20: 245-260.
29. Rosen, R. 1958b. The representation of biological systems from the standpoint of the theory of categories. Bull. Math. Biophys. 20:317-342.
30. Rosen, R. 1959. A relational theory of biological systems, II. Bull. Math. Biophys. 21:109-127.