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Entropy 2014, 16(6), 3379-3400; doi:10.3390/e16063379

Coarse Dynamics for Coarse Modeling: An Example From Population Biology

Received: 23 March 2014 / Revised: 29 May 2014 / Accepted: 6 June 2014 / Published: 19 June 2014
(This article belongs to the Special Issue Information in Dynamical Systems and Complex Systems)
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Networks have become a popular way to concisely represent complex nonlinear systems where the interactions and parameters are imprecisely known. One challenge is how best to describe the associated dynamics, which can exhibit complicated behavior sensitive to small changes in parameters. A recently developed computational approach that we refer to as a database for dynamics provides a robust and mathematically rigorous description of global dynamics over large ranges of parameter space. To demonstrate the potential of this approach we consider two classical age-structured population models that share the same network diagram and have a similar nonlinear overcompensatory term, but nevertheless yield different patterns of qualitative behavior as a function of parameters. Using a generalization of these models we relate the different structure of the dynamics that are observed in the context of biologically relevant questions such as stable oscillations in populations, bistability, and permanence.
Keywords: database for dynamics; conley theory; population model database for dynamics; conley theory; population model
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Bush, J.; Mischaikow, K. Coarse Dynamics for Coarse Modeling: An Example From Population Biology. Entropy 2014, 16, 3379-3400.

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