Parametric sensitivity of system stability in chemical dynamics

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Abstract
A combined stability–sensitivity analysis is implemented to probe the details of the solutions of systems of ordinary differential equations arising in chemical dynamics. The dynamical Green’s function matrix is calculated and then diagonalized to yield the stability eigenvalues and eigenvectors. The latter eigenvectors prescribe the combinations of state variables (respectively, concentrations in kinetics or coordinates and momenta in classical mechanics) giving rise to the stable or unstable motion as indicated by the associated eigenvalues. In addition, the sensitivities of the eigenvalues and eigenvectors are calculated. This approach provides pertinent information regarding the response of system stability to the relevant physical parameters. Model problems from homogeneous chemical kinetics and classical molecular dynamics are studied using this analysis. The additional information available is discussed in comparison with other approaches to stability analysis.