%0 Journal Article %1 evans2004structural %A Evans, N.D. %A Chappell, M.J. %A Chapman, M.J. %A Godfrey, K.R. %D 2004 %J Automatica %K dynamical_systems identifiability %N 11 %P 1947 - 1953 %R http://dx.doi.org/10.1016/j.automatica.2004.06.002 %T Structural indistinguishability between uncontrolled (autonomous) nonlinear analytic systems %U http://www.sciencedirect.com/science/article/pii/S0005109804001700 %V 40 %X In this paper, an approach for analysing the structural indistinguishability between two uncontrolled (or autonomous) analytic systems is presented. The approach involves constructing, if possible, a smooth mapping between the trajectories of two candidate models. If either of the models satisfies an observability criterion, then such a transformation always exists when the models are indistinguishable from their outputs. The approach is illustrated by examples from epidemiology and chemical reaction kinetics. One important outcome is that the susceptible, infectious, recovered (SIR) and \SIR\ with temporary immunity (SIRS) models are shown to be indistinguishable when a proportion of the number of infectives is measured.

@article{evans2004structural, abstract = {In this paper, an approach for analysing the structural indistinguishability between two uncontrolled (or autonomous) analytic systems is presented. The approach involves constructing, if possible, a smooth mapping between the trajectories of two candidate models. If either of the models satisfies an observability criterion, then such a transformation always exists when the models are indistinguishable from their outputs. The approach is illustrated by examples from epidemiology and chemical reaction kinetics. One important outcome is that the susceptible, infectious, recovered (SIR) and \{SIR\} with temporary immunity (SIRS) models are shown to be indistinguishable when a proportion of the number of infectives is measured. }, added-at = {2016-07-01T07:08:54.000+0200}, author = {Evans, N.D. and Chappell, M.J. and Chapman, M.J. and Godfrey, K.R.}, biburl = {https://www.bibsonomy.org/bibtex/2dcf3b49a76a02ea740819a0b224f7dcc/peter.ralph}, doi = {http://dx.doi.org/10.1016/j.automatica.2004.06.002}, interhash = {7502609f4e30ad2078c71e1441291a8e}, intrahash = {dcf3b49a76a02ea740819a0b224f7dcc}, issn = {0005-1098}, journal = {Automatica }, keywords = {dynamical_systems identifiability}, number = 11, pages = {1947 - 1953}, timestamp = {2016-07-01T07:08:54.000+0200}, title = {Structural indistinguishability between uncontrolled (autonomous) nonlinear analytic systems }, url = {http://www.sciencedirect.com/science/article/pii/S0005109804001700}, volume = 40, year = 2004 }