  The observational ubiquity of inverse power law spectra (IPL) in complex
phenomena entails theory for dynamic fractal phenomena capturing their fractal
dimension, dynamics, and statistics. These and other properties are
consequences of the complexity resulting from nonlinear dynamic networks
collectively summarized for biomedical phenomena as the Network Effect (NE) or
focused more narrowly as Network Physiology. Herein we address the measurable
consequences of the NE on time series generated by different parts of the
brain, heart, and lung organ networks, which are directly related to their
inter-network and intra-network interactions. Moreover, these same physiologic
organ networks have been shown to generate crucial event (CE) time series, and
herein are shown, using modified diffusion entropy analysis (MDEA), to have
scaling indices with quasiperiodic changes in complexity, as measured by
scaling indices, over time. Such time series are generated by different parts
of the brain, heart, and lung organ networks, and the results do not depend on
the underlying coherence properties of the associated time series but
demonstrate a generalized synchronization of complexity. This high order
synchrony among the scaling indices of EEG (brain), ECG (heart), and
respiratory time series is governed by the quantitative interdependence of the
multifractal behavior of the various physiological organs' network dynamics.
This consequence of the NE opens the door for an entirely general
characterization of the dynamics of complex networks in terms of complexity
synchronization (CS) independently of the scientific, engineering, or
technological context.
