Linear response of a time-periodic state

Publisher Website
Google Scholar
Abstract
The authors consider the linear response from a time-periodic state. For additive external forces, the susceptibility matrix is diagonalised in the time domain. Multiplicative coupling is also discussed. Measuring the eigen-response, i.e. the response to a force parallel to an eigenvector of the susceptibility matrix, provides a test for the model used to describe the system. It enables them to determine the different Floquet exponents of the time-periodic state. These indicate the stability range of the solution and give a lower bound for the number of relevant variables involved in the dynamics of the system. The eigen-response associated with a critical Floquet exponent exhibits a resonant behaviour in the vicinity of the corresponding instability that gives rise to a bifurcation from the time-periodic state.