Application of joint singularity spectrum to analyze cooperative dynamics of complex systems

Abstract

Purpose of this work is to generalize the wavelet-transform modulus maxima method to the case of cooperative dynamics of interacting systems and to introduce the joint singularity spectrum into consideration. The research method is the wavelet-based multifractal formalism, the generalized version of which is used to quantitatively describe the effect of chaotic synchronization in the dynamics of model systems. Models of coupled Rossler systems and paired nephrons are considered. As a result of the studies carried out, the main changes in the joint singularity spectra were noted during the transition from synchronous to asynchronous oscillations in the first model and to the partial synchronization mode in the second model. Conclusion. Proposed approach can be used in studies of the cooperative dynamics of systems of various nature.