Analysis of Complex Cooperative Dynamics Using Joint Singularity Spectrum

The paper deals with a generalization of the wavelet transform modulus maxima method for the analysis of the cooperative dynamics of systems including interacting components. The paper presents a generalized wavelet-based multifractal formalism, which is used to quantitatively describe the effect of synchronizing chaos in the dynamics of model systems. Models of coupled Rössler systems and paired nephrons were considered, and changes in the joint singularity spectra during the transition from synchronous to nonsynchronous oscillations in the first model and to the partial synchronization mode in the second model were noted. The results of the study allow us to use the proposed approach to analyze the cooperative dynamics of systems of different nature.