Skip to main content
Log in

Some algebraic properties of (M, R)-systems

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

On the basis of Rosen's representation of (M, R)-systems as sequential machines (Rosen,Bull. Math. Biophys.,26, 103–111, 1964), the existence of projective limits in categories of general (M, R)-systems is proved.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Arbib, M. 1966. “Categories of (M, R)-Systems.”Bull. Math. Biophysics,28, 511–517.

    Article  Google Scholar 

  • Băianu, I. 1970. “Organismic Supercategories: II. On Multistable Systems.” —Ibid.,,32, 539–561.

    Article  Google Scholar 

  • Băianu, I. 1971. “Categories, Functors and Automata Theory.”The Fourth Int. Congress L.M.P.S., Bucharest, August–September 1971.

  • Băianu, I. and M. Marinescu. 1973. “A Functorial Construction of (M, R)-Systems.”Rev. Roum. Math. Pures et Appl. (in press).

  • Căzănescu, V. 1967. “On the Category of Abstract Sequential Automata” (paper in Romanian followed by summary in French and Russian),Ann. Univ. Bucharest, Math. and Mechanics Series,16, No. 1, 31–37.

    Google Scholar 

  • Demetrius, L. 1966. “Abstract Biological Systems as Sequential Machines: Behavioral Reversibility.”Bull. Math. Biophysics,28, 153–160.

    Article  Google Scholar 

  • Foster, B. L. 1966. “Re-establishability in Abstract Biology.” —Ibid.,,28, 371–374.

    Article  Google Scholar 

  • Freyd, P. 1964.Abelian Categories. An Introduction to the Theory of Functors.” New York: Harper & Row.

    MATH  Google Scholar 

  • Mitchell, B. 1965.The Theory of Categories. New York and London: Academic Press.

    Google Scholar 

  • Rosen, Robert. 1958a. “A Relational Theory of Biological Systems.”Bull. Math. Biophysics,20, 245–260.

    Article  Google Scholar 

  • —. 1958b. “The Representation of Biological Systems from the Standpoint of the Theory of Categories.” ——Ibid.,,20, 317–342.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • —. 1961. “A Relational Theory of Structural Changes Induced in Biological Systems by Alterations in Environment.” ——Ibid.,,23, 165–171.

    Article  Google Scholar 

  • —. 1962. “A Note on Abstract Relational Biologies.” —Ibid.,,24, 31–38.

    Article  Google Scholar 

  • —. 1963a. “On the Reversibility of Environmentally Induced Alterations in Abstract Biological Systems.” ——Ibid.,,25, 41–50.

    Article  Google Scholar 

  • —. 1963b. “Some Results in Graph Theory and Their Application to Abstract Relational Biology.” —Ibid.,,25, 231–241.

    Article  Google Scholar 

  • —. 1964a. “Abstract Biological Systems as Sequential Machines.” —Ibid.,,26, 103–111.

    Article  Google Scholar 

  • —. 1964b. “Abstract Biological Systems as Sequential Machines II: Strong Connectedness and Reversibility.”—Ibid.,,26, 239–246.

    Article  Google Scholar 

  • —. 1966a. “Abstract Biological Systems as Sequential Machines: III. Some Algebraic Aspects.”—Ibid.,,28, 141–148.

    Article  Google Scholar 

  • —. 1966b. “A Note on Replication in (M, R)-Systems.” —Ibid.,,28, 149–151.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • —. 1971. “Some Realizations of (M, R)-Systems and Their Interpretation.”Bull. Math. Biophysics,33, 303–319.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Băianu, I. Some algebraic properties of (M, R)-systems. Bltn Mathcal Biology 35, 213–217 (1973). https://doi.org/10.1007/BF02558807

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02558807

Keywords

Navigation