General Sensitivity Analysis of Differential Equation Systems

Abstract

Sensitivity analysis is generally concerned with probing the relationship between the dependent and independent variables in mathematical modelling problems. The motivation behind seeking such information can be quite diverse, depending on the circumstances. Firstly, in many systems the para-meters or independent variables are imprecisely known, and knowledge of how this imprecision affects output (observables) is of considerable interest. Secondly, even in cases where the system input is precisely known the actual dynamics can obscure knowledge of which portions of the input control the relevant system observables. Thirdly, one may view all of the system variables, both dependent and independent, as forming a large set from which their original identities may be interchanged, depending on the physical questions of concern. Finally, there is the overriding issue of global para-meter space mapping whereby one would like to understand how the system behaves with regard to excursions in a finite region of parameter space. All of these issues may be addressed by appropriate sensitivity techniques [1], although some of the matters are easier to treat than others. In particular, the available practical sensitivity techniques tend to be local in nature, and global parameter mapping may remain an inherently difficult problem. For the most part, the present paper will not deal with the latter issue.