Complex fluctuations and robustness in stylized signalling networks

Abstract

Complex fluctuations with correlations involving multiple scales appear in many physical,social and biological systems. In particular, in physiological systems the degree of complexity,measured in terms of the exponent of the time correlations of the fluctuations, is alteredwith disease and ageing. Here, we show that correlated fluctuations characterized by1/f scaling of their power spectra can emerge from networks of simple signalling units. Weanalyse networks of simple signalling units where the type of scaling of the fluctuationsis associated with (i) a complex topology with a discrete and sparse number ofrandom links between units, (ii) a restricted set of nonlinear interaction rules, and(iii) the presence of noise. Furthermore, we find that changes in one or more ofthese properties leads to degradation of the correlation properties. Moreover,changes in the microscopic construction of the model do not produce qualitativechanges in the dynamical behaviour, showing hence the robustness of our findings.