Metering effects in population systems

Erika T. Camacho; Christopher M. Kribs-Zaleta; Stephen Wirkus

doi:10.3934/mbe.2013.10.1365

Article Contents

2013, Volume 10, Issue 5&6: 1365-1379. Doi: 10.3934/mbe.2013.10.1365 open access

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Metering effects in population systems

1.
School of Mathematical & Natural Sciences, Arizona State University, 4701 W. Thunderbird Rd, Glendale, AZ, 85306
2.
Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408

Received: August 2012

Revised: December 2012

Published: July 2013

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Abstract

This study compares the effects of two types of metering (periodic resetting and periodic increments) on one variable in a dynamical system, relative to the behavior of the corresponding system with an equivalent level of constant recruitment (influx). While the level of the target population in the constant-influx system generally remains between the local extrema of the same population in the metered model, the same is not always true for other state variables in the system. These effects are illustrated by applications to models for chemotherapy dosing and for eating disorders in a school setting.

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Mathematics Subject Classification: Primary: 00A71, 37N25; Secondary: 92D25.

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