paper

Self-organized criticality: An explanation of the 1/f noise

  • Authors:
Read the paper

📜 Abstract

A simple mathematical model which exhibits self-organized criticality, hence also 1/f noise, is proposed. It manifests the same process of dynamic scaling found in the growth of deposition surfaces and in percolation. In the model, regions of stability are punctuated by abrupt reorganizations in which those regions are restructured to accommodate the instability engendered by critical fluctuations. The present model is similar to models of interface depinning, the Edwards-Wilkinson model, and models of dynamic surfaces. Applications to a wide variety of phenomena are possible.

✨ Summary

This foundational paper introduces the concept of self-organized criticality (SOC) to explain the occurrence of 1/f noise in various systems. The authors propose a simple mathematical model, which, akin to the sandpile model, demonstrates how systems naturally evolve to a critical state — a state in which a minor event can trigger significant consequences. This model aligns with phenomena observed in dynamic scaling and percolation.

The paper has had a profound impact on the study of complex systems, influencing a wide range of fields from geology to neuroscience, where the SOC concept has been applied to explain various complex phenomena.

Notably, it has been cited extensively, serving as a fundamental reference in subsequent research related to critical phenomena, emergent behavior, and power laws in natural and social systems. For instance, the concept has been utilized in understanding earthquake dynamics, brain activity patterns, and even in stock market fluctuations. Citations include:

  1. Turcotte, D. L. (1999). Self-organized criticality. Reports on Progress in Physics. Link
  2. Jensen, H. J. (1998). Self-organized criticality: Emergent complex behavior in physical and biological systems. Cambridge University Press.
  3. Beggs, J. M. (2007). Seeking the neural code with evocative time series. Elsevier. Link

Through these and other citations, it is evident that Bak, Tang, and Wiesenfeld’s work has played a pivotal role in advancing our understanding of self-organizing systems and continues to be influential in both theoretical and applied research.