Cooperative dynamics of complex systems studied with joint singularity spectra

Abstract

Complex systems often include interacting components that can exhibit complex behavior. A change in the dynamics of such systems is a consequence of a change in the functioning of individual components or the connections between them. In the latter case, it is important to obtain information about the cooperative dynamics of elements of a complex system (for example, a complex network) using quantitative criteria that reflect the interaction of subsystems. The dynamics of individual elements can demonstrate a multifractal structure. For its quantitative description, a single value reflecting the features of the frequency dependence of the spectral power density or the decay of correlations is not enough. When conducting research, an approach based on the calculation of the singularity spectrum is often used. Generalization of the concept of multifractals to the case of cooperative dynamics of complex systems requires estimating joint multifractal measures. In this study we consider a generalization to the case of joint dynamics of systems with self-sustained oscillations of the wavelet-transform modulus-maxima method, in which wavelet functions are selected as elements of the coverage. This makes it possible to use a quite universal approach applicable both to stationary processes and to signals of systems with time-varying characteristics.

This work was supported by the Russian Science Foundation (Agreement 22-22-00065).

Speaker

German A. Guyo
Saratov State University
Russia

Discussion

Ask question