Abstract
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a dynamical regime between order and disorder attain the highest level of computational capabilities and achieve an optimal trade-off between robustness and flexibility. Recent results in cellular and evolutionary biology, neuroscience and computer science have revitalised the interest in the criticality hypothesis, emphasising its role as a viable candidate general law in adaptive complex systems. This paper provides an overview of the works on dynamical criticality that are — To the best of our knowledge — Particularly relevant for the criticality hypothesis. The authors review the main contributions concerning dynamics and information processing at the edge of chaos, and illustrate the main achievements in the study of critical dynamics in biological systems. Finally, the authors discuss open questions and propose an agenda for future work.
Highlights
The peculiar properties of critical systems are at the roots of a conjecture stating that systems in a dynamical regime between order and disorder optimally balance robustness and adaptiveness, and reliably respond to inputs while being capable to react with a wide repertoire of possible actions
SOC is certainly relevant for the study of complex systems, but in this review we are mainly concerned with the phenomenon of dynamical criticality: in this case, there are qualitatively different dynamical behaviours corresponding to different parameter values, and the critical points separate regions in parameter space that correspond to different behaviours
The peculiar properties of critical systems enlightened in thermodynamics and statistical physics are at the roots of a conjecture stating that systems at the phase transition achieve the highest level of computational capability
Summary
The peculiar properties of critical systems are at the roots of a conjecture stating that systems in a dynamical regime between order and disorder optimally balance robustness and adaptiveness, and reliably respond to inputs while being capable to react with a wide repertoire of possible actions. This conjecture was proposed by Kauffman [40, 41] with main focus on living systems and by Packard, Langton and Crutchfield [65, 49, 20] who introduced the expression “computation at the edge of chaos”.
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