Modes of growth in dynamic systems

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Publication Type pre-print
School or College College of Mines & Earth Sciences
Department Meteorology
Creator Garrett, Timothy J.
Title Modes of growth in dynamic systems
Date 2012-01-01
Description Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how system growth can be constrained to a few distinct modes that depend on the time integral of past flows and the current availability of material and energetic resources. These modes include a law of diminishing returns, logistic behavior and, if resources are expanding very rapidly, super-exponential growth. For a case where a system has a resolved sink as well as a source, growth and decay can be characterized in terms of a slightly modified form of the predator-prey equations commonly employed in ecology, where the perturbation formulation of these equations is equivalent to a damped simple harmonic oscillator. Thus, the framework presented here suggests a common theoretical under-pinning for emergent behaviors in the physical and life sciences. Specific examples are described for phenomena as seemingly dissimilar as the development of rain and the evolution of fish stocks.
Type Text
Publisher Royal Society Publishing
Volume 468
Issue 2145
First Page 1
Last Page 17
Language eng
Bibliographic Citation Garrett, T. J. (2012). Modes of growth in dynamic systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468(2145), 1-17.
Rights Management (c)Royal Society
Format Medium application/pdf
Format Extent 310,695 bytes
Identifier uspace,17740
ARK ark:/87278/s6nw2tbj
Setname ir_uspace
Date Created 2014-05-19
Date Modified 2014-05-19
ID 712557
Reference URL https://collections.lib.utah.edu/ark:/87278/s6nw2tbj
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