TOPOLOGICAL METHODS FOR SOCIAL AND BEHAVIORAL SYSTEMS†

Partial support for this paper was provided by the U.S. Department of Energy under Contract No. DE-AC01-80RA50260.

Abstract

Methods based in algebra and geometry are introduced for the mathematical formulation of problems in the social and behavioral sciences. Specifically, the paper introduces the main concepts of singularity theory, catastrophe theory and q-analysis for the characterization of the global structure of social systems. Applications in urban land development, electric power generation and international conflict are given to illustrate the methodology. The paper concludes with an outline for a general mathematical theory of surprises, together with a program for investigating the systemic property of resilience.

INDEX TERMS:

• Singularity theory
• catastrophe theory
• resilience
• q-analysis

Notes

Partial support for this paper was provided by the U.S. Department of Energy under Contract No. DE-AC01-80RA50260.

Additional information

Notes on contributors

JOHN CASTI

John Casti is currently a research mathematician at the International Institute for Applied Systems Analysis, Laxenburg, Austria and Professor, Department of Systems Engineering, University of Arizona,Tucson, Arizona. Previously, Dr.Casti held professorships at NewYork University,Princeton University and SUNY, Binghampton, I as well as research positions at Systems Control, Inc. and the Rand Corporation. Dr. Casti received his Ph.D. in Mathematics (1970) at the University of Southern California under Professor R. E. Bellman and has pursued research interests in control theory. dynamic programming, numerical solution of boundary-value problems and integral equations. His current research interests arc in the areas of dynamical system theory and its applications in natural resource problems arc the social and behavioural sciences. In addition to over 75 research articles, Dr. Casti has also authored several research monographs including Dynamical Systems and their Applications in Linear Theory (Academic Press, 1977), Connectivity, Complexity and Catastrophe in Large Systems (Wiley-Interscience, 1979) and Principles of Dynamic Programming, vols. I and II. (with R. Larson. Dekker. 1978, 1982). In addition. Dr. Casti edits the journal Applied Mathematics and Compulation (Elsevier) and the two book series. Control and System Theory (Dekker) and Frontiers of Systems Research in the Social Sciences (Nijhoff).