Inverse-affine dependence of recovery-time sensitivities on critical disturbance parameters: A nonlinear dynamics explanation

We study the sensitivity properties of non-linear dynamical systems subject to disturbances, when disturbance parameters are near critical values. In particular, in seeking to explain recent experimental and simulation results, we give an explanation for why the inverses of response-time sensitivities to disturbance parameters often display an affine dependence on the parameters near critical points. Application of the results in electrical power system analysis and virus-spreading control examples are presented.