State Aggregation and Population Dynamics in Linear Systems

Authors:
Jonathan E. Rowe;Michael D. Vose;Alden H. Wright
Affiliations:
School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK;Computer Science Department, University of Tennessee, Knoxville, TN 37996;Department of Computer Science, University of Montana, Missoula, Montana 59812
Venue:
Artificial Life
Year:
2005

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Abstract

We consider complex systems that are composed of many interacting elements, evolving under some dynamics. We are interested in characterizing the ways in which these elements may be grouped into higher-level, macroscopic states in a way that is compatible with those dynamics. Such groupings may then be thought of as naturally emergent properties of the system. We formalize this idea and, in the case that the dynamics are linear, prove necessary and sufficient conditions for this to happen. In cases where there is an underlying symmetry among the components of the system, group theory may be used to provide a strong sufficient condition. These observations are illustrated with some artificial life examples.