Mathematical Biosciences and Engineering, 2007, 4(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

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.
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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

 

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