Sensitivity analysis of oscillatory systems

Methods of sensitivity analysis are extended to find the parametric dependencies of systems of ordinary differential equations which exhibit limit cycle oscillations. The quantitative relations between the system parameters and the observable period, amplitude, phase and cycle shape are developed. These formulae, presented for both the first and second order, are applicable to systems of arbitrary size and complexity. The techniques are used here to develop correlations for period and amplitude in a non-isothermal oscillating stirred-tank chemical reactor, and to find and optimize a beneficial periodic operating strategy for a lumped-parameter catalytic reacting system.