Mathematical Biosciences and Engineering, 2013, 10(5&6): 1365-1379. doi: 10.3934/mbe.2013.10.1365.

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

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

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

This study compares the effects of two types of metering (periodic resettingand periodic increments) on one variable in a dynamical system, relative to thebehavior of the corresponding system with an equivalent level of constantrecruitment (influx). While the level of the target population in theconstant-influx system generally remains between the local extrema of the samepopulation in the metered model, the same is not always true for other statevariables in the system. These effects are illustrated by applications tomodels for chemotherapy dosing and for eating disorders in a school setting.
  Figure/Table
  Supplementary
  Article Metrics

Keywords bulimia.; Metered model; drug dosing; dynamical systems; discontinuities

Citation: Erika T. Camacho, Christopher M. Kribs-Zaleta, Stephen Wirkus. Metering effects in population systems. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1365-1379. doi: 10.3934/mbe.2013.10.1365

References

  • 1. Mathematical and Computer Modelling, 50 (2009), 481-997.
  • 2. Aequationes Mathematicae, 69 (2005), 83-96.
  • 3. Biometrics Unit Technical Report BU-1522-M, Cornell University, 1999. Available from: http://mtbi.asu.edu/.
  • 4. 2006. Available from: http://www.public.asu.edu/ etcamach/AMSSI/reports/alcohol2006.pdf.
  • 5. Ellis Horwood, Chichester, 1989.
  • 6. Longman, Harlow, 1993.
  • 7. Springer, New York, 2012.
  • 8. Springer-Verlag, 2003.
  • 9. $2^{nd}$ edition, Springer, Berlin, 1999.
  • 10. Journal of Vibration and Control, 6 (2000), 61-83.
  • 11. Ph.D. thesis, Center for Applied Mathematics, Cornell University, Ithaca, NY, 2003.
  • 12. Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 3086-3097.
  • 13. Journal of Scheduling, 6 (2003), 251-267.
  • 14. Ecological Modelling, 127 (2000), 1-9.
  • 15. Physics of Life Reviews, 5 (2008), 50-77.
  • 16. Journal of Computer and System Sciences, 2380 (2003), 183-197.
  • 17. Theoretical Population Biology, 72 (2007), 197-213.
  • 18. Journal of Mathematical Biology, 28 (1990), 365-382.
  • 19. Applied Mathematics Letters, 18 (2005), 729-732.
  • 20. Journal of Theoretical Biology, 230 (2004), 521-532.
  • 21. Vaccine, 24 (2006), 6037-6045.
  • 22. Journal of Biomedicine and Biotechnology, 2007, Article ID 64870, 10 pp.
  • 23. Journal of Mathematical Psychology, 47 (2003), 515-526.
  • 24. Theoretical Population Biology, 49 (1996), 265-290.
  • 25. Ecology, 81 (2000), 3330-3340.
  • 26. Nonlinear Analysis: Real World Applications, 2 (2001), 455-465.
  • 27. World Scientific, Singapore, 1989.
  • 28. Journal of Computational and Applied Mathematics, 174 (2005), 227-238.
  • 29. Natural Resource Modeling, 20 (2007), 549-574.
  • 30. arXiv:1008.2534.
  • 31. Journal of Vibration and Control, 17 (2011), 1869-1885.
  • 32. Theoretical Population Biology, 70 (2006), 174-182.
  • 33. Journal of Vibration and Control, 4 (1998), 61-74.
  • 34. Proceedings of the 40th IEEE Conference on Decision and Control, 3 (2001), 2247-2252.
  • 35. Proceedings of the American Mathematical Society, 125 (1997), 2599-2604.
  • 36. Nonlinear Analysis: Real World Applications, 10 (2009), 680-690.
  • 37. Bulletin of Mathematical Biology, 58 (1996), 425-447.
  • 38. Mathematical Biosciences, 147 (1998), 41-61.
  • 39. Theoretical Population Biology, 66 (2004), 151-161.
  • 40. Mathematical Medicine and Biology, 8 (1991), 83-93.
  • 41. Mathematical Medicine and Biology, 9 (1992), 29-41.
  • 42. Journal of Mathematical Biology, 37 (1998), 272-290.
  • 43. World Scientific, Singapore, 1995.
  • 44. Journal of Studies on Alcohol and Drugs, 70 (2009), 805-821.
  • 45. Bulletin of Mathematical Biology, 60 (1998), 1-26.
  • 46. Princeton University Press, Princeton, 1986.
  • 47. Journal of Vibration and Control, 17 (2011), 81-101.
  • 48. Mathematical Biosciences, 180 (2002), 29-48.
  • 49. Springer, New York, 2001.
  • 50. Mathematical and Computer Modelling, 40 (2004), 509-518.
  • 51. Mathematical and Computer Modelling, 39 (2004), 479-493.
  • 52. Nonlinear Analysis: Real World Applications, 9 (2008), 1714-1726.
  • 53. Nonlinear Analysis: Real World Applications, 4 (2003), 639-651.

 

Reader Comments

your name: *   your email: *  

Copyright Info: 2013, Erika T. Camacho, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved