Renewal intermittency in complex systems

Day - Time: 02 July 2014, h.11:00
Place: Area della Ricerca CNR di Pisa - Room: C-29
  • Paolo Paradisi ()

Umberto Barcaro


The interest towards self-organized and cooperative systems has rapidly increased in recent years. This is related to the increasing interest in the evolution of complex networks, such as the web and, more in general, social dynamics (not only associated with web applications), but also biological applications such as neural networks, human brain dynamics and metabolic networks in the cell. This hot research field is sometimes denoted as complexity science.
A fully accepted definition of â??complex systemâ?? does not yet exist, but thereâ??s some agreement on some general features. A complex system is typically made of many individual units with strong non-linear interactions and the global dynamics of this multi-component system is characterized by emergent properties, i.e., the emergence of cooperative, self-organized, coherent structures that are hardly explained in terms of microscopic dynamics. Thus, the typical approach is focused on emergent properties and their dynamical evolution.
Along this line, a crucial property that has been observed is given by the meta-stability of the emerging self-organized structures, that is, the dynamics of a complex system is characterized by a birth-death process of cooperation [Allegrini et al., 2009]. In time series analysis, this is mathematically described in the framework of point processes and, in particular, of renewal theory [Cox, 1962]. A renewal process is a sequence of critical short-time events, with abrupt memory decays, thus dividing the time series into separate segments with long-range memory [Paradisi et al., 2013; Allegrini et al., 2013; Fingelkurts et al., 2008]. As a consequence, the inter-event times are statistically distributed according to a inverse power-law, a condition also denoted as fractal intermittency. The sequence of renewal events with fractal distribution of inter-event times are associated with anomalous diffusion processes.
Here we will show how simple random walks driven by complex (i.e., fractal intermittent) events generate anomalous diffusion and long-range correlation despite the presence of memory erasing events in the time series. Then, we discuss different approaches for the statistical characterization of diffusion scaling in time series with intermittent events. We discuss the robustness of diffusion scaling generated by event-driven random walks with respect to the presence of noisy events, here modelled as events with Poisson statistics, as such events are not able to generate anomalous diffusion, but only normal diffusion (i.e., variance linearly increasing in time).

[l] Allegrini et al., Physical Review E 80, 061914 (2009).
[2] D.R. Cox, Renewal Theory Ed.: Methuen, London (1962).
[3] Paradisi et al., AIP Conf. Proc. 1510, 151-161 (2013).
[4] Allegrini et al., Chaos Solit. Fract. 55, 32-43 (2013).
[5] Fingelkurts and Fingelkurts, Open Neuroimaging J. 2, 73-93 (2008).