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A numerical study of synchronization in the process of biochemical substance exchange in a diffusively coupled ring of cells

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Mihailović D., Balaž I., Arsenić I.
Open Physics
|
2013
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vol. 11
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issue 4
440-447
EN
In this paper we numerically investigate a model of a diffusively coupled ring of cells. To model the dynamics of individual cells we propose a map with cell affinity, which is a generalization of the logistic map. First, the basic features of a one-cell system are studied in terms of the Lyapunov exponent, Kolmogorov complexity and Sample Entropy. Second, the notion of observational heterarchy, which is a perpetual negotiation process between different levels of the description of a phenomenon, is reviewed. After these preliminaries, we study how the active coupling induced by the consideration of the observational heterarchy modifies the synchronization property of the model with N=100 cells. It is shown numerically that the active coupling enhances synchronization of biochemical substance exchange in several different conditions of cell affinity.
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Novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis

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Mihailović D. T., Mimić G., Nikolić-Djorić E., Arsenić I.
Open Physics
|
2015
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vol. 13
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issue 1
EN
We propose novel metrics based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We consider the origins of the Kolmogorov complexity and discuss its physical meaning. To get better insights into the nature of complex systems and time series analysis we introduce three novel measures based on the Kolmogorov complexity: (i) the Kolmogorov complexity spectrum, (ii) the Kolmogorov complexity spectrum highest value and (iii) the overall Kolmogorov complexity. The characteristics of these measures have been tested using a generalized logistic equation. Finally, the proposed measures have been applied to different time series originating from: a model output (the biochemical substance exchange in a multi-cell system), four different geophysical phenomena (dynamics of: river flow, long term precipitation, indoor 222Rn concentration and UV radiation dose) and the economy (stock price dynamics). The results obtained offer deeper insights into the complexity of system dynamics and time series analysis with the proposed complexity measures.
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