Method and apparatus for detecting nonlinearity and chaos in a dynamical system

摘要

Methods and apparatus are provided for detecting the presence of a nonlinear characteristic of an autonomous (i.e., non-driven and time- invariant), dynamical system and for determining whether such nonlinear dynamical system is chaotic. First, a system is determined to be either nonlinear or linear. If the system is determined to be nonlinear, then noise of increasing intensity is incrementally added to a data set representing the analyzed system until the resulting test signal appears to be linear. If the noise limit of the resulting test signal is significantly greater than zero, then the system is determined to be chaotic and the amount of noise added to the data set provides an indication of the relative strength of the chaos. Alternatively, if the noise limit of the resulting test signal is approximately zero, then the system is determined to be nonlinear with periodic or quasi-periodic limit cycles. An optional power spectrum test is described with which it can be confirmed that the system is nonlinear with periodic or quasi- periodic limit cycles.