Mathematical Biosciences and Engineering, 2007, 4(3): 403-430. doi: 10.3934/mbe.2007.4.403.

34A34, 34K05, 49Q12, 34K30.

Export file:


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


  • Citation Only
  • Citation and Abstract

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

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.
  Article Metrics

Keywords nonlinear dynamical systems with uncertain parameters; differential equations with distributional delays; sensitivity with respect to probability measures; approximation.

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


This article has been cited by

  • 1. H. T. Banks, Sava Dediu, Stacey L. Ernstberger, Franz Kappel, Generalized sensitivities and optimal experimental design, Journal of Inverse and Ill-posed Problems, 2010, 18, 1, 10.1515/jiip.2010.002
  • 2. Karyn L. Sutton, Danielle Robbins, H.Thomas Banks, Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations, Mathematical Biosciences and Engineering, 2013, 10, 5/6, 1301, 10.3934/mbe.2013.10.1301
  • 3. H. T. Banks, Danielle Robbins, Karyn L. Sutton, , Control and Optimization with PDE Constraints, 2013, Chapter 2, 19, 10.1007/978-3-0348-0631-2_2
  • 4. H. Thomas Banks, Marie Davidian, John R. Samuels, Karyn L. Sutton, , Mathematical and Statistical Estimation Approaches in Epidemiology, 2009, Chapter 11, 249, 10.1007/978-90-481-2313-1_11
  • 5. H. T. Banks, S. Dediu, S. L. Ernstberger, Sensitivity functions and their uses in inverse problems, Journal of Inverse and Ill-posed Problems, 2007, 15, 7, 10.1515/jiip.2007.038
  • 6. H. T. Banks, J. E. Banks, S. L. Joyner, Estimation in time-delay modeling of insecticide-induced mortality, Journal of Inverse and Ill-posed Problems, 2009, 17, 2, 10.1515/JIIP.2009.012
  • 7. V. V. Uchaikin, V. A. Litvinov, Variational Interpolation of Functionals in Transport Theory Inverse Problems, Numerical Analysis and Applications, 2019, 12, 3, 297, 10.1134/S199542391903008X

Reader Comments

your name: *   your email: *  

Copyright Info: 2007, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved