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The space-lumped two-variable neuron model is studied. Extension of the neural model by adding a simple synaptic current allows the demonstration of neural interactions. The production of synchronous burst activity in this simple two-neuron excitatory loop is modeled, including the influence of random background excitatory input. The ability of the neuron model to integrate inputs spatially and temporally is shown. Two refractory periods after stimuli were identified and their role in burst cessation is demonstrated. Our findings show that simple neural units without long-lasting membrane processes are capable of generating long lasting patterns of activity. The results of simulation of simple background activity suggest that an increase in background activity tends to cause decreased activity of the network. This phenomenon, as well as the existence of two refractory periods, allows for burst cessation without inhibition in this simple model.

Herein we address the measurable consequences of the network effect (NE) on time series generated by different parts of the brain, heart, and lung organ-networks (ONs), which are directly related to their inter-network and intra-network interactions. Moreover, these same physiologic ONs 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 ONs, 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 ONs’ 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. CS is truly a transdisciplinary effect.

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