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Mathematical Biosciences and Engineering

2007, Volume 4, Issue 3: 403-430. doi: 10.3934/mbe.2007.4.403
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Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space

  • 1.
    Center for Research in Scientific Computation and Department of Mathematics, North Carolina State University, Raleigh, NC
  • Received: 01 November 2006 Accepted: 29 June 2018 Published: 01 May 2007

  • MSC : 34A34, 34K05, 49Q12, 34K30.

  • We develop a theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space. Specific motivating examples for probability measure dependent differential, partial differential and delay differential equations are given. Schemes that approximate the measures in the Prohorov sense are illustrated with numerical simulations for distributed delay differential equations.

    Citation: H.T. Banks, S. Dediu, H.K. Nguyen. Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space[J]. Mathematical Biosciences and Engineering, 2007, 4(3): 403-430. doi: 10.3934/mbe.2007.4.403

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  • We develop a theory for sensitivity with respect to parameters in a convex subset of a topological vector space of dynamical systems in a Banach space. Specific motivating examples for probability measure dependent differential, partial differential and delay differential equations are given. Schemes that approximate the measures in the Prohorov sense are illustrated with numerical simulations for distributed delay differential equations.


  • This article has been cited by:

    1. H. T. Banks, J. E. Banks, S. L. Joyner, Estimation in time-delay modeling of insecticide-induced mortality, 2009, 17, 0928-0219, 10.1515/JIIP.2009.012
    2. V. V. Uchaikin, V. A. Litvinov, Variational Interpolation of Functionals in Transport Theory Inverse Problems, 2019, 12, 1995-4239, 297, 10.1134/S199542391903008X
    3. H. Thomas Banks, Marie Davidian, John R. Samuels, Karyn L. Sutton, 2009, Chapter 11, 978-90-481-2312-4, 249, 10.1007/978-90-481-2313-1_11
    4. H. T. Banks, Sava Dediu, Stacey L. Ernstberger, Franz Kappel, Generalized sensitivities and optimal experimental design, 2010, 18, 0928-0219, 10.1515/jiip.2010.002
    5. H. T. Banks, Danielle Robbins, Karyn L. Sutton, 2013, Chapter 2, 978-3-0348-0630-5, 19, 10.1007/978-3-0348-0631-2_2
    6. H. T. Banks, S. Dediu, S. L. Ernstberger, Sensitivity functions and their uses in inverse problems, 2007, 15, 0928-0219, 10.1515/jiip.2007.038
    7. Karyn L. Sutton, Danielle Robbins, H.Thomas Banks, Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations, 2013, 10, 1551-0018, 1301, 10.3934/mbe.2013.10.1301
    8. H. Banks, Stacey Ernstberger, Shuhua Hu, Sensitivity equations for a size-structured population model, 2009, 67, 0033-569X, 627, 10.1090/S0033-569X-09-01105-1
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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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