Abstract
A numerical tool, sensitivity analysis, which can be used to study the effects of parameter perturbations on systems of dynamical equations is briefly described. A straightforward application of the methods of sensitivity analysis to ordinary differential equation models for oscillating reactions is found to yield results which are difficult to physically interpret. In this work it is shown that the standard sensitivity analysis of equations with periodic solutions yields an expansion that contains secular terms. A Lindstedt-Poincare approach is taken, instead, and it is found that physically meaningful sensitivity information can be extracted from the straightforward sensitivity analysis results, in some cases. In the other cases, it is found that structural stability/instability can be assessed with this modification of sensitivity analysis. Illustration is given for the Lotka-Volterra oscillator.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D. Edelson, R.M. Noyes and R.J. Field, Intl. J. Chem. Kin. 11, 155 (1979)
D. Edelson and H. Rabitz, “Numerical Techniques for Modeling and Analysis of Oscillating Reactions”, manuscript in preparation for Oscillations and Traveling Waves in> Chemica Systems, R. J. Field and M. Burger, eds.
D. Sattinger, Topics in Stability and Bifurcation Theory, Springer- Verlag, New York (1973)
D. Edelson and V.M. Thomas, “Sensitivity Analysis of Oscillating Reactions. 1. The Period of the Oregonator”, J. Phys. Chem. 85, 1555 (1981)
R. Larter, H. Rabitz and M. Kramer, “Sensitivity Analysis of Limit Cycles”, submitted to J. Chem. Phys., (1983)
R. Larter, “Sensitivity Analysis of Autonomous Oscillators: Separation of Secular Terms and Determination of Structural Stability”, in press, J. Phys. Chem. (1983)
P.M. Frank, Introduction to System Sensitivity Theory, Academic Press, New York (1978)
R. Tomovic and M. Vukobratovic, General Sensitivity Theory, Elsevier, New York (1972)
J.T. Hwang, E.P. Dougherty, S. Rabitz and H. Rabitz, “The Green’s Function Method of Sensitivity Analysis in Chemical Kinetics”, J. Chem. Phys. 69, 5180 (1978)
A.H. Nayfeh, Introduction to Perturbation Techniques, Wiley, New York (1981)
M. Demiralp and H. Rabitz, “Chemical Kinetic functional sensitivity analysis: Elementary sensitivities”, J. Chem. Phys. 74, 3362 (1981)
R. Larter, H. Rabitz and M. Kobayashi, “Derived sensitivity densities in chemical kinetics: A new computational approach with applications”, in press, J. Chem. Phys. (1983)
L. Eno and H. Rabitz, “Generalized sensitivity analysis in quantum collision theory”, J. Chem. Phys. 71, 4824 (1979)
R. Larter and H. Rabitz, “Scattering Theory Sensitivity Analysis for Spatial Hamiltonian Variations”, submitted to J. Chem. Phys. (1983)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1984 D.Reidel Publishing Company
About this chapter
Cite this chapter
Larter, R. (1984). Sensitivity Analysis: A Numerical Tool for the Study of Parameter Variations in Oscillating Reaction Models. In: Nicolis, G., Baras, F. (eds) Chemical Instabilities. NATO ASI Series, vol 120. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7254-4_4
Download citation
DOI: https://doi.org/10.1007/978-94-009-7254-4_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-7256-8
Online ISBN: 978-94-009-7254-4
eBook Packages: Springer Book Archive