Multidimensional measures of response and fluctuations in stochastic dynamical systems

摘要

Aclass of experiments is proposed which involve multiple measurements combinedwith multiple perturbationsnof a nonlinear classical complex system. A family of multipoint n + m − 1 dimensional measures R(n,m) thatnprovide complementary information on complex systems is obtained by combining m nonlinear stimuli and nnmeasurements. They represent the combined effect of causal response and noncausal spontaneous fluctuations.nThe proposed signals can be measured either in the frequency domain or in the time domain. Generalizednfluctuation-dissipation relations which hold in the nonlinear regime restrict the number of independent techniques.nTwo-dimensional correlation plots derived from such measurements can reveal various types of couplings amongncollective modes.