1U' . . . . ~"'nlU'u" AND JORDI BASCOMPTE PHASE TRANSITIONS AND ORDER PARAMETERS oWto define complexity is not a trivial question. Several definitions have been proposed, and all of them share the intuitive idea that complexity is neither complete order nor complete disorder [1-5]. But this statement, though fairly intuitive, is far from satisfactory. A quantitative characterization of complexity is necessary. Which "universal" features share apparently different complex systems? The behavior of physical systems close to critical points may answer this question. It is well known, from the theory of phase transitions, that a given system (possibly made of many subsystems) can undergo strong qualitative changes in its macroscopic properties if a suitable control parameter is adequately tuned and that close to these critical points some key characteristic constants (the so-called critical exponents) are the same for very different systems . At critical points, fractal structures, complex dynamical patterns and optimal information transfer appear in a spontaneous way. Observing such properties in those systems which we call "complex," we can conjecture that complexity tends to appear close to instability points. In this paper, two main types of theoretical approximations are considered': (i) continuous dynamical systems, possibly including
Complexity – Wiley
Published: Mar 1, 1996
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