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Hierarchical behavior in fit dynamical systems

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Abstract

We consider a class of differentiable dynamical systems that fulfill a criterion of adaptation, or beingfit. The adaptation criterion is found to be sufficient for the existence of hierarchical behavior in these systems, once they become complex. Commutative diagram methods are used to show that under reasonable conditions the hierarchical behavior takes the form of a closed dynamics of aggregate variables. This dynamics characterizes the system functions as a whole. Existence conditions for the aggregate dynamics are obtained, together with their differential form and their connections to the original system description. The results indicate that evolutionary processes are likely to produce systems that are hierarchically organized in term of their function as well as their structure.

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  1. Department of Medicine, University of Toronto, Toronto, Canada

    Charles J. Lumsden

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  1. Charles J. Lumsden
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Lumsden, C.J. Hierarchical behavior in fit dynamical systems. Bltn Mathcal Biology 47, 591–612 (1985). https://doi.org/10.1007/BF02460128

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