A Theory of Cell-to-Cell Mapping Dynamical Systems

[+] Author and Article Information
C. S. Hsu

Department of Mechanical Engineering, University of California, Berkeley, Calif. 94720

J. Appl. Mech 47(4), 931-939 (Dec 01, 1980) (9 pages) doi:10.1115/1.3153816 History: Received May 01, 1980; Revised June 01, 1980; Online July 21, 2009


The method of point-to-point mappings has been receiving increasing attention in recent years. In this paper we discuss instead dynamical systems governed by cell-to-cell mappings. The justifications of considering such mappings come from the unavoidable accuracy limitations of both physical measurements and numerical evaluation. Because of these limitations one is not really able to treat a state variable as a continuum of points but rather only as a collection of very small intervals. The introduction of the idea of cell-to-cell mappings has led to an algorithm which is found to be potentially a very powerful tool for global analysis of dynamical systems. In this paper an introductory theory of cell-to-cell mappings is offered. The theory provides a basis for the algorithm presented in [14]. In the first half of the paper we discuss the analysis of cell-to-cell mappings in their own right. In the second half the cell-to-cell mappings which are obtained from point-to-point mappings by discretization are examined in order to see what properties of the point mapping systems are preserved in the discretization process.

Copyright © 1980 by ASME
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