Evolution in complex systems

Abstract

What features characterise complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena[1-3]. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analysed to confirm this effect. The strain arises from local frustration. As the strain is released through "quakes", some system variable undergoes record statistics with accompanying log-Poisson statistics for the quake event times[4]. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology, and show how quantitative indications of ageing can be found.Comment: 8 pages, 5 figures all in one fil

<title>Extremal noise events, intermittency, and Log-Poisson statistics in non-equilibrium aging of complex systems</title>

“…driven dissipative systems, 27, 29 and biological evolution. 17,21,28,52,53 Broadly speaking, the physical mechanism behind all these examples combines an entropic Figure 9. The empirical distribution for the log waiting times numerically obtained for the ROM and the Tangled Nature model 17, 51 is shown.…”

“…The emphasis is on general ideas, and the original papers [16][17][18][19][20] should be consulted for further details.…”

Logarithmically slow onset of synchronization

“…Log-Poisson processes have been observed in the NK model of evolution (Sibani & Pedersen 1999), charge-density waves (Sibani & Littlewood 1993), and further in spin glasses, supercooled magnet relaxation, and the Tangled Nature evolution model (Anderson et al 2004). While in a Poisson process the probabilities for events t k are characterized by (van Kampen 2007):…”

Comment on P. Nouvellet, J.P. Bacon, D. Waxman, “Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model”

“…In record dynamics, events are triggered when a fluctuating, record, signal exceeds a historical 'high water mark'. While exponential decay is characterised by Poisson statistics in linear time, record dynamics are characterised by Poisson statistics in logarithmic time (Sibani and Littlewood, 1993;Anderson et al, 2004). Our results demonstrate that under both experimental conditions the process of ants exiting their nests is compatible with a record dynamics process (Richardson et al, 2010a).…”