Abstract
The relationships that define the structure of a given ecosystem, social system, or even a physiological function can only exist if certain parameters are confined to a certain range of values. As the values change and exceed this given range the relationships are forced to change, and so produce a new pattern of relationships. The concept of a dynamic structure captures this potential for structural change in relation to a set of parameters. The precise definition of structure and allowable transformation constitutes the definition of a category. The total range of parameters associated with all the relevant structures provides a parameter space which is assumed to be a manifold. Maps with extra structure from the manifold to the category define dynamic structures. The domain of differential dynamic systems is the manifold, and a flow or movement across the manifold is associated with a series of structural transformations in the category. In some cases a structure outruns its parameter range, to be faced with an obstruction—an absence of possible transformations. Ways of studying such “obstructions” are considered along with the related problem of extending a dynamic structure beyond a previously given set of parameters. The cost or resistance of transformations is also studied. The concepts of dynamic structures are illustrated by the structural change of food webs and they are used in a necessarily qualitative fashion to study dominance structures of social orders and finally to speculate on the qualitative nature of evolutionary change of functional aspects of organisms.
Similar content being viewed by others
Literature
Arbib, M. A. and E. G. Manes 1975.Arrows, Structures and Functors. The Categorical Imperative. New York: Academic Press.
Chepko-Sade, D. 1979. “Monkey Group Splits Up.”New Scientist 82, 348–350.
Eldredge, N., and S. J. Gould. 1972. “Punctuated Equilibria: an Alternative to Phyletic Gradualism.” InModels in Paleobiology, Ed. Schopf J. J. M., pp. 82–115. San Francisco: Freeman, Cooper & Co.
Gallopin, G. C. 1972. “Structural Properties of Food Webs.” In,Systems Analysis and Simulation in Ecology, Ed. Patten, B., Vol. 2. New York: Academic Press.
Johnstone, P. 1977.Topos Theory. New York: Academic Press.
Leguizamon, C. A. 1975. “Concept of Energy in Biological Systems.”Bull. Math. Biol. 37, 565–572.
Mumay Tansky. 1976. “Structure Stability and Efficiency of Ecosystems.” In:Progress in Theoretical Biology, Ed. Rosen R. and Snell F. M. Vol. 4. New York: Academic Press.
Palis, J. 1968. “On Morse-Smale Diffeomorphisms.”Bull. Amer. Math. Soc. 74, 985–987.
Patten, B. C. 1972. “Variable-Structure Aspects of Ecosystems”, InTheory and Applications of Variable Structure Systems, Eds. Mohler R. R. and Ruberti A. New York: Academic Press.
Rosen, R. 1971. “Some Realisations of (M, R)-Systems and Their Interpretation.”Bull. Math. Biophys. 33, 303–319.
Smale, S. 1967. “Differentiable Dynamical Systems.”Bull. Am. Math. Soc. 73, 747–817.
Thom, R. 1975.Structural Stability and Morphogenesis. Reading, MA: W. A. Benjamin.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
MacFarlane, A.I. Dynamic structure theory: A structural approach to social and biological systems. Bltn Mathcal Biology 43, 579–591 (1981). https://doi.org/10.1007/BF02462314
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02462314