Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space

Abstract. In this paper we consider the classical Sinko-Streifer size-structured population model and derive sensitivity partial differential equations for the sensitivities of solutions with respect to initial conditions, growth rate, mortality rate and fecundity rate. Sample numerical results to illustrate the use of these equations are also presented. [3,4,29,32] have focused on establishing well-posedness and stability analysis of models, formulating schemes for numerical solutions, and parameter estimation of individual rates. However, to the best of our knowledge, thus far there is no literature on sensitivity equations and the related analysis for size-structured population models. Sensitivity analysis of dynamical systems has drawn the attention of numerous researchers [1,6,9,10,11,13,14,15,16,17,20,24,25,27,28,35,38,40] for many years because the resulting sensitivity functions can be used in many areas such as optimization and design [16,26,27,34,38], computation of standard errors [9,10,19,21,36], and information theory [12] related quantities (e.g., the Fisher information matrix) as well as control theory, parameter estimation and inverse problems [5,8,9,10,11,40,41]. One of our motivations for investigating sensitivity for size-structured population models derives from our efforts reported in [7], where a shrimp biomass production system and a

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Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space

Cited by 14 publications

References 59 publications

Generalized Sensitivity Analysis for Delay Differential Equations

Generalized Sensitivity Analysis for Delay Differential Equations

An Inverse Problem Statistical Methodology Summary

Sensitivity equations for a size-structured population model

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