10.2190/DKK9-QGT1-7DH0-2G3U DKK9QGT17DH02G3U 5 A Simple Model of Self-Regulation in Large Natural Hierarchical Systems 281 289 20020509 20020509 20020509 20020509 DKK9QGT17DH02G3U.pdf http://baywood.metapress.com/link.asp?target=contribution&id=DKK9QGT17DH02G3U 3 I. A. Lubashevskii V. V. Gafiychuk Academy of Technology Science of Russian Federation, Russia Institute for Applied Problems of Mechanics and Mathematic, Ukranian Academy of Sciences, Ukraine The characteristics of large hierarchical systems existing in nature are discussed from the standpoint of self-regulation problems. By way of example, some biophysical, ecological and economic systems are considered. A cooperative mechanism of self-regulation which enables the system to function ideally is proposed. A mathematical model for large hierarchical system involving a basic medium and hierarchical transport network responding to variations in the basic medium parameters are formulated. The governing equations that describe evolution of this system in terms of two continuous fields are presented. The meaning of these fields are discussed for different natural systems. A. Shitzer and R. C. Eberhart (eds.), <i>Heat Transfer in Medicine and Biology, Anal. and Appl., 1, 2</i>, Plenum, New York, 1985. G. I. Mchedlishvili, <i>Microcirculation of Blood, General Principles of Control and Disturbances</i>, Nauka, Leningrad, 1989. (in Russian). <i>Reading in Microeconomics</i>, W. Breit, H. M. Hodrman, and E. Saueracker (eds.), Times Mirror/Mosby College Publishing, 1985. R. E. Ulanowicz, <i>Growth and Development: Ecosystems Phenomenology</i>, Springer-Verlag, New York, 1986. S. E. Jorgensen, <i>Integration of Ecosystem Theories: A Pattern</i>, Kluwer Academic Publishers, 1992. P. A. Samuelson, <i>Foundations of Economic Analysis</i>, Harvard University Press, Cambridge, 1947. G. Nicolis and I. Prigogine, <i>Self-organization in Nonequilibrium Systems</i>, Wiley, New York, 1977.