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An inverse-cascade model for self-organized critical behavior

Author

Listed:
  • Turcotte, D.L.
  • Malamud, B.D.
  • Morein, G.
  • Newman, W.I.

Abstract

We introduce an inverse-cascade model to explain self-organized critical behavior. This model is motivated by the forest-fire model. In the forest-fire model trees are randomly planted on a grid, sparks are also dropped on the grid resulting in fires in which trees are lost. In the inverse-cascade model single trees are introduced and these combine to form larger and larger clusters. This is the inverse cascade and gives a power-law (fractal) frequency-size distribution of clusters. Model fires eliminate trees from all cluster sizes but significant numbers of trees are lost only from the largest clusters and this loss terminates the power-law scaling. Finally, our model illustrates important differences between critical and self-organized critical behavior.

Suggested Citation

  • Turcotte, D.L. & Malamud, B.D. & Morein, G. & Newman, W.I., 1999. "An inverse-cascade model for self-organized critical behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(3), pages 629-643.
    • Handle: RePEc:eee:phsmap:v:268:y:1999:i:3:p:629-643
    DOI: 10.1016/S0378-4371(99)00092-8
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    Citations

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    Cited by:

    1. Zaliapin, Ilia & Kovchegov, Yevgeniy, 2012. "Tokunaga and Horton self-similarity for level set trees of Markov chains," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 358-372.
    2. Turcotte, Donald L & Malamud, Bruce D, 2004. "Landslides, forest fires, and earthquakes: examples of self-organized critical behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(4), pages 580-589.
    3. Mauro, John C. & Diehl, Brett & Marcellin, Richard F. & Vaughn, Daniel J., 2018. "Workplace accidents and self-organized criticality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 284-289.
    4. Noskov, M.D. & Malinovski, A.S. & Sack, M. & Schwab, A.J., 2001. "Self-organized criticality in electrical treeing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 85-96.
    5. Wang, Jian & Song, Weiguo & Zheng, Hongyang & Telesca, Luciano, 2010. "Temporal scaling behavior of human-caused fires and their connection to relative humidity of the atmosphere," Ecological Modelling, Elsevier, vol. 221(1), pages 85-89.

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