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Mathematical Biosciences and Engineering (MBE)
 

Metering effects in population systems

Pages: 1365 - 1379, Volume 10, Issue 5/6, October/December 2013      doi:10.3934/mbe.2013.10.1365

 
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Erika T. Camacho - School of Mathematical & Natural Sciences, Arizona State University, 4701 W. Thunderbird Rd, Glendale, AZ, 85306, United States (email)
Christopher M. Kribs-Zaleta - Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, United States (email)
Stephen Wirkus - School of Mathematical & Natural Sciences, Arizona State University, 4701 W. Thunderbird Rd, Glendale, AZ, 85306, United States (email)

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.

Keywords:  Metered model, discontinuities, dynamical systems, drug dosing, bulimia.
Mathematics Subject Classification:  Primary: 00A71, 37N25; Secondary: 92D25.

Received: August 2012;      Accepted: December 2012;      Available Online: August 2013.

 References