Aging and self-organized criticality in driven dissipative systems

Group dynamics and record signals in the ant Temnothorax albipennis

Many purely physical complex systems, in which there are both stochasticity and local interactions between the components, exhibit record dynamics. The temporal statistics of record dynamics is a Poisson process operating on a logarithmic rather than a linear time scale (i.e. a log-Poisson process). Record dynamics often drive substantial changes in complex systems when new high water marks in partially stochastic processes trigger new events. Social insect colonies are exemplary complex biological systems in which many of the local interactions of the components have been moulded by natural selection for the common good. Here, we combine experimental manipulation of ant colony demography with modelling to test the hypothesis that social interactions are the mechanism underlying the record dynamics. We found that compared with the control, log-Poisson statistics were disrupted in colonies in which the pattern of interactions was modified by the removal of the brood, and disappeared completely in 'callow' colonies composed entirely of very young workers from the same age cohort. We conclude that a subtle interplay between the demography of the society and the pattern of the interactions between the ants is crucial for the emergence of record dynamics. This could help identify what makes an ant colony a cohesive society.

Devil's-staircase-like behavior of the range of random time series with record-breaking fluctuations

We propose insight into the analysis of the record-breaking fluctuations in random time series, which permits to distinguish between the self-organized criticality and the record dynamics (RD) scenarios of system evolution, using a finite time series realization. Performed analysis of the time series associated with the historical prices of different commodities has shown that the evolution of commodity markets is controlled by the record-breaking fluctuations as it is outlined by the RD. Furthermore, we found that the sizes of record-breaking fluctuations follow a fat-tailed distribution and the devil's-staircase-like records of price ranges are multiaffine and persistent, nevertheless, the high moments (q> q(C) >2) of their q-order height-height correlation functions behave logarithmically.