Skip to main content
SpringerLink
Log in

Organismic supercategories and qualitative dynamics of systems

  • Published:
The bulletin of mathematical biophysics Aims and scope Submit manuscript

Abstract

The representation of biological systems by means of organismic supercategories, developed in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–71;32, 539–561), is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Băianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete result concerning dynamics of genetic system, development, fertilization, regeneration, analogies, and oncogenesis are derived.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Ashby, W. R. 1956.An Introduction to Cybernetics, New York: J. Wiley & Sons, Inc.

    MATH  Google Scholar 

  • Băianu, I. and M. Marinescu. 1968. “Organismic Supercategories: I. Proposals for a General Unitary Theory of Systems.”Bull. Math. Biophysics,30, 625–636.

    MATH  Google Scholar 

  • Băianu, I. and M. Marinescu. 1969a. “Cell Synchrony and Control.”Abstracts of the Third International Biophysics Congress, M.I.T., IX4-Cybernetics, 148.

  • Băianu, I. 1969b. “Changes of Cellular Controls in Oncogenesis: the Hypothesis of Resonant Transfer of Energy.”The Fifth Biophysics Symposium, Bucharest, Romania.

  • Băianu, I. 1970. “Organismic Supercategories: III. On Multistable Systems”Bull. Math. Biophysics,32, December, No. 4.

    Google Scholar 

  • Bellman, R. 1968. “Dynamic Programming and Modern Control Theory.”Proceedings of International Congress of Mathematics, Moscow—1966, 65–82, Moscow: “Mir” Printing House.

    MATH  Google Scholar 

  • Bourbaki, N. 1964.Eléments de Mathématique, Livre II,Algébre, 4, Paris: Hermann, Editeur.

    Google Scholar 

  • Comoroşan, A. and I. Băianu. 1969. “Abstract Representations of Biological Systems in Supercategories.”Bull. Math. Biophysics,31, 59–71.

    MATH  Google Scholar 

  • Ehresmann, Ch. 1966. “Trends Toward Unity in Mathematics.”Cahiers de topologie et geometrie diffentielle,8, 1–7.

    Google Scholar 

  • Eilenberg, S. and S. MacLane. 1945. “General Theory of Natural Equivalences.”Trans. Am. Math. Soc.,58, 231–294.

    Article  MATH  MathSciNet  Google Scholar 

  • Hodge, W. and D. Pedoe. 1968.Methods of Algebraic Geometry. Cambridge: Cambridge University Press.

    Google Scholar 

  • Hwa, R. and V. Teplitz. 1966.Homology and Feynman Integrals, New York, Amsterdam: W. A. Benjamin, Inc.

    MATH  Google Scholar 

  • Jacob, F. and J. Monod. 1961. “On the Regulation of Gene Activity.” InCold Spring Harbor Symposia on Quantitative Biology,26, 193–211, New York: Leonora Frisch, ed.

    Google Scholar 

  • —et al. 1963. “Regulation of DNA Reduplication in Bacteria.”Ibid. In28, 323–376.

    Google Scholar 

  • MacLane, S. 1963.Homology. Berlin-Göttingen-Heidelberg: Springer-Verlag.

    MATH  Google Scholar 

  • Mattuck, R. 1967.A Guide to Feynman Diagrams in the Many-Body Problem. London-New York-Toronto-Sydney: McGraw-Hill Publishing Company Limited.

    Google Scholar 

  • Poincaré, Henri. 1881. “Sur les courbes définies par une équation différentielle.”Oeurves complètes,1, Paris: Gauthier-Villars.

    Google Scholar 

  • Peixoto, M. 1967.Quanlitative Theory of Differential Equations and Structural Stability, Differential Equations and Dynamical Systems. New York: Academic Press.

    Google Scholar 

  • Rashevsky, Nicholas. 1956a. “Geometrization of Biology.”Bull. Math. Biophysics 18, 31–56.

    MathSciNet  Google Scholar 

  • —. 1956b. “Contribution to Topological Biology: Some Considerations on the Primordial Graph and on some Possible Transformations.”Ibid.,18, 113–128.

    MathSciNet  Google Scholar 

  • —. 1966a. “Physics, Biology and Sociology: a Reappraisal”Ibid. 28, 283–308.

    MathSciNet  Google Scholar 

  • —. 1966b. “A Sociological Approach to Biology.”Ibid. 28, 655–661.

    MathSciNet  Google Scholar 

  • —. 1967a. “Organismic Sets: Outline of a General Theory of Biological and Social Organisms.”Ibid.,29 139–152.

    MATH  Google Scholar 

  • —. 1967b “Organismic Sets and Biological Epimorphism.”Ibid. 29, 389–393.

    Google Scholar 

  • —. 1967c. “Physics, Biology and Sociology: II. Suggestion for a Synthesis.”Ibid.,29, 643–648.

    Google Scholar 

  • —. 1968a. “Organismic Sets II: Some General Considerations.”Ibid.,30, 163–173.

    MATH  Google Scholar 

  • — 1968b. “A Note on the Development of Organismic Sets.”Ibid. 30, 355–358.

    Google Scholar 

  • —. 1968c. “Neurocybernetics as a Particular Case of General Regulatory Mechanisms in Biological and Social Organisms.”Age de la Science,3, 243–258.

    Google Scholar 

  • —. 1969. “Outline of a Unified Approach to Physics, Biology and Sociology.”Bull. Math. Biophysics,31, 159–198.

    MATH  Google Scholar 

  • Rosen, Robert. 1958a. “A Relational Theory of Biological Systems.”Bull. Math. Biophysics,20, 317–342.

    Google Scholar 

  • Rosen, Robert. 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories.”Ibid.,20, 245–260.

    Google Scholar 

  • —. 1959. “A Relational Theory of Biological Systems II.”Ibid.,,21, 109–127.

    Google Scholar 

  • —. 1960. “A Quantum-Theoretic Approach to Genetic Problems.”Ibid.,22, 227–255.

    Google Scholar 

  • —. 1968a. “On Analogous Systems.”Ibid.,30, 481–492.

    MATH  Google Scholar 

  • —. 1968b. “Recent Developments in the Theory of Control and Regulation of Cellular Processes.”Int. Review of Cytology,23, 25–88.

    Article  Google Scholar 

  • —. 1968c. “Relational Biology and Cybernetics.” InBiokybernetik. 49–56. Leipzig: Karl Marx-Universität, Drischel, H. and Tiedt, N., eds.

    Google Scholar 

  • Sen, D. K.. 1968.Fields and/or Particles. London and New York: Academic Press.

    Google Scholar 

  • Takahashi, S. 1969.Analysis in Categories. Kingston, Ontario: Queen’s University.

    MATH  Google Scholar 

  • Thom, René. 1969. “Topological Models in Biology.”Topology,8, 313–335.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Physics Dept. of Electricity, University of Bucharest, Str Academiei nr. 14, Bucharest, Romania

    I. Băianu

Authors
  1. I. Băianu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Băianu, I. Organismic supercategories and qualitative dynamics of systems. Bulletin of Mathematical Biophysics 33, 339–354 (1971). https://doi.org/10.1007/BF02476778

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02476778

Keywords

Search

Navigation