The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.
Nonlinear dynamical systems often appear to have uncorrelated output. This characteristic leads to the idea of analyzing the dynamics of nonlinear systems with methods developed for random processes. The Karhunen-Loe`ve-Transform (KLT) was designed to detect coherent structures in random process data. It can also be applied for state monitoring of complex systems. This paper gives a short review on the mathematical concept of the KLT and discusses an approach to characterize the dynamics of nonlinear systems based on experimental data.
Black-box identification and simulation of continuous-time nonlinear systems with random processes