Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations
In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and genera...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1301 |
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| author | H.Thomas Banks Danielle Robbins Karyn L. Sutton |
| author_facet | H.Thomas Banks Danielle Robbins Karyn L. Sutton |
| author_sort | H.Thomas Banks |
| collection | DOAJ |
| description | In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems. |
| format | Article |
| id | doaj-art-e531d66fe8a04821a7f3a984ff817e1f |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e531d66fe8a04821a7f3a984ff817e1f2025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61301133310.3934/mbe.2013.10.1301Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equationsH.Thomas Banks0Danielle Robbins1Karyn L. Sutton2Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212Center for Research in Scientific Computation, Center for Quantitative Sciences in Biomedicine, Raleigh, NC 27695-8212In this paper we present new results for differentiability of delay systems with respect to initial conditions and delays. After motivating our results with a wide range of delay examples arising in biology applications, we further note the need for sensitivity functions (both traditional and generalized sensitivity functions), especially in control and estimation problems. We summarize general existence and uniqueness results before turning to our main results on differentiation with respect to delays, etc. Finally we discuss use of our results in the context of estimation problems.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1301delay equationsfisher information matrix.differentiability with respect to delayssensitivitygeneralized sensitivity |
| spellingShingle | H.Thomas Banks Danielle Robbins Karyn L. Sutton Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations Mathematical Biosciences and Engineering delay equations fisher information matrix. differentiability with respect to delays sensitivity generalized sensitivity |
| title | Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations |
| title_full | Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations |
| title_fullStr | Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations |
| title_full_unstemmed | Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations |
| title_short | Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations |
| title_sort | theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations |
| topic | delay equations fisher information matrix. differentiability with respect to delays sensitivity generalized sensitivity |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1301 |
| work_keys_str_mv | AT hthomasbanks theoreticalfoundationsfortraditionalandgeneralizedsensitivityfunctionsfornonlineardelaydifferentialequations AT daniellerobbins theoreticalfoundationsfortraditionalandgeneralizedsensitivityfunctionsfornonlineardelaydifferentialequations AT karynlsutton theoreticalfoundationsfortraditionalandgeneralizedsensitivityfunctionsfornonlineardelaydifferentialequations |