creators_name: Baianu, I.C. creators_id: icb editors_name: Rashevsky, Nicolas type: journalp datestamp: 2011-12-16 00:58:54 lastmod: 2011-12-16 00:58:54 metadata_visibility: show title: Organismic Supercategories: III. Qualitative Dynamics of Systems ispublished: pub subjects: bio-theory subjects: comp-neuro-sci subjects: comp-sci-art-intel subjects: comp-sci-complex-theory subjects: comp-sci-mach-dynam-sys subjects: comp-sci-neural-nets subjects: neurgen subjects: neuro-chem full_text_status: public keywords: Quantum Computation,Quantum Automata, Carcinogenesis, Categories and Functors, Homology Theory, Quantum Genetics, Relational Oscillations, Organismic Supercategories, Qualitative Dynamics, Algebraic Geometry in Biology, Dynamic Programnming, Categorical Dynamic Systems, Observables Generating Diagram, Relational Biology note: Supercategories defined currently as n-categories or higher dimensional algebra, Axiomatic definitions of Categories and Supercategories of Relational, Complex Biological Systems, Dynamic Computations with Algebraic Varieties, Cell Transformations to Malignant Cancer. abstract: The representation of biological systems by means of organismic supercategories, developed in previous papers, is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Baianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete results concerning dynamics of genetic system, development, fertilization, regeneration, analogies, and oncogenesis are derived. date: 1971-11-21 date_type: published publication: The Bulletin of Mathematical Biophysics volume: 33 number: 3 publisher: Elsevier Publs. Co. and Springer reprints pagerange: 339-354 refereed: TRUE referencetext: The author is indebted to Professor Nicholas Rashevsky for helpful suggestions. Also the author would like to thank Professor Robert Rosen for sending materials pertinent to this work. LITERATURE Ashby, W.R. 1956. An Introduction to Gybernetics, New York: J. Wiley & Sons, Inc. Baianu, I. and M. Marinescu. 1968. "Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems," Bull. Math. Biophysics, 30, 625-636. Baianu, I. and M. Marinescu. 1969a. "Cell Synehrony and Control." Abstracts of the Third International Biophysics Congress, M.I.T., IX4-Cybernetics, 148. 1969b. "Changes of Cellular Controls in Oneogenesis: the Hypothesis of Resonant Transfer of Energy." The Fifth Biophysics Symposium, Bucharest, Romania. Baianu, I. 1970. "Organismic Supereategories: III. On Multistable Systems." Bull. Math. Biophysics, $2, December, :No. 4. Bellman, R. 1968. "Dynamic Programming and Modern Control Theory." Proceedings of International Congress of Mathematics, Moscow--1966, 65-82, Moscow: "Mir" Printing House. Bourbaki, N. 1964. Eldments de Math~matique, Livre II, Algdbre, 4, Paris: Hermarm, Editeur. Comoro~an, S. and I. B~ianu. 1969. "Abstract Representations of Biological Systems in Supercategories." Bull. Math. Biophysics, SI, 59-71. Ehresmann, Ch. 1966. "Trends Toward Unity in Mathematics." Cahiers de topologie et geometric differentieUe, 8, 1-7. Eilenberg, S. and S. MacLane. 1945. "General Theory of Natural Equivalences." Trans. Am. Math. See., 58, 231-294. Hedge, W. and D. Pedoe. 1968. Methods of Algebraic Geometry. Cambridge: Cambridge University Press. Hwa, R. and V. Teplitz. 1966. Homology and 2'eynman Integrals, New York, Amsterdam: W. A. Benjamin, Inc. Jacob, F. and J. Monod. 1961. "On the Regulation of Gene Activity." In Cold Spring Harbor Symposia on Quantitative Biology, 26, 193-211, New York: Leonora Frisch, ed. - - et al. 1963. "Regulation of DNA Reduplication in Bacteria." Ibid., 28, 323-376. MacLane, S. 1963. Homology. Berlin-G6ttingen-Heidelberg: Springer-Verlag. Mattuek, R. 1967. A Guide to Feynman Diagrams in the Many-Body Problem. London- New York-Toronto-Sydney: McGraw-Hill Publishing Company Limited. Poincar~, Henri. 1881. "Sur les courbes d6finies par une ~quation diff~rentielle." Oeuvres completes, 1, Paris: Gauthier-Villars. Peixoto, M. 1967. Qualitative Theory of Differential Equations and Structural Stability, Differential Equations and Dynamical Systems. New York: Academic Press. Rashevsky, Nicholas. 1956a. "Geometrization of Biology." Bull. Math. Biophysics 18, 31-56. 19561). "Contribution to Topological Biology: Some Considerations on the Primordial Graph and on some l~ossible Transformations." Ibid., 18, 113-128. 1966a. "Physics, Biology and Sociology: a Reappraisal." Ibid., 28, 283-308. 1966b. "A Sociological Approach to Biology." Ibid., 28, 655-661. 1967a. "Organismic Sets: Outline of a General Theory of Biological and Social Organisms." Ibid., 29, 139-152. 1967b. "Organismic Sets and Biological Epimorphism." 15/d., 29, 389-393. 1967c. "Physics, Biology and Sociology: II. Suggestion for a Synthesis." Ibid., 29, 643-648. 1968a. "Organismic Sets II: Some General Considerations." !bid., $6, 163- 173. 1968b. "A :Note on the Development of Organismic Sets." Ibid., 30, 355-358. 1968c. "Neurocybernetics as a Particular Case of General Regulatory Mechanisms in Biological and Social Organisms." Age de la Science, 3, 243-258. 1969. "Outline of a Unified Approach to Physics, Biology and Sociology." Bull. Math. Biophysics, 31, 159-198. Rosen, Robert. 1958a. "A Relational Theory of Biological Systems." Bull. Math. Biophysics, 20, 317-342. citation: Baianu, Prof. Dr. I.C. (1971) Organismic Supercategories: III. Qualitative Dynamics of Systems. [Journal (Paginated)] document_url: http://cogprints.org/7743/1/ORganismic_supercategories_and_qualitative_dynamics_of_systems_final3.pdf document_url: http://cogprints.org/7743/4/OSqualDyn.pdf document_url: http://cogprints.org/7743/10/ORganismic_supercategories_and_qualitative_dynamics_of_systems_final3.pdf