Condition of a "dynamical system with extended spatial degrees of freedom in two or three dimensions" which "naturally evolves into a self-organized critical state" (P. BAK, C. TANG & K. WIESENFELD, 1988, p.365).
The authors state:"By self organized we mean that the system naturally evolves to the state without detailed specification of the initial conditions (i.e. the critical state is an attractor of the dynamics). Moreover, the critical state is robust with respect to variations of parameters, and the presence of quenched randomness" (Ibid).
However more recently P. BAK and K. CHEN state; "… composite systems may never reach equilibrium but instead evolve from one meta stable state to the next" (1991, p. 26). They add:"During the past four years, experiments and models have demonstrated that many composite systems at the heart of geology, economy, biology, and meteorology show signs of self-organized criticality. These insights have improved our understanding of the behavior of the earth's crust, stock markets, ecosystems and many other composite systems" (Ibid).
Self-organized criticality has two "signatures" or "fingerprints" in P. BAK's and al. terms:
- a spatial ones which appears as a fractal structure specified by a power-law
- a temporal one which corresponds in each case to a specific flicker-noise
These abstract explanations become clearer when connected with ASHBY's concepts of ultrastability, non determined transformation and transition's probabilities matrix, all related to composite systems (See his :"Introduction to Cybernetics").
St. KAUFFMAN uses the criticality model in the co-evolution dynamics of populations (1993, p.256).
P. BAK comments: "… regularity of catastrophic events, fractals, 1/f noise, and Zipf's law – are so similar, in that they can all be expressed as straight lines on a double logarithmic plot, that they make us wonder if they are all manifestations of a single principle…. – Maybe self-organized criticality is that single underlying principle.
"Self-organized critical systems evolve to the complex critical state without interference from any outside agent.
The process of self-organization takes place over a very long transient period. Complex behavior, whether in geophysics of biology, is always created by a long process of evolution. It cannot be understood by studying the system within a time frame that is short compared with this evolutionary process. The phrase "you cannot understand the present without understanding history" takes on a deeper and more precise meaning (1996, p.31).
BAK also observes that "self-organized criticality can actually be thought of as the theoretical underpinning for catastrophism, the oposite philosophy to gradualism" (Ibid, p.131).
Both views are useful in their own way, for instance in evolution theory. BAK writes: "If the theory of self-organized criticlity is applicable, then the dynamics of avalanches represent the link between DARWIN's view of continuous evolution and the punctuations representing sudden quantitative and qualitative changes. Sandpiles are driven by small changes but they nevertheless exhibit large catastrophic events" (Ibid).
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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