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DY: Fachverband Dynamik und Statistische Physik

DY 19: Statistical Physics 4 - organized by Barbara Drossel (Darmstadt), Sabine Klapp (Berlin) and Thomas Speck (Mainz)

DY 19.4: Talk

Tuesday, March 23, 2021, 10:00–10:20, DYb

On the dynamics of the Forest Fire Model — •Diego Rybski^1,2 and Jan W. Kantelhardt³ — ¹Potsdam Institute for Climate Impact Research – PIK, Member of Leibniz Association, P.O. Box 601203, 14412 Potsdam, Germany — ²Department of Environmental Science Policy and Management, University of California Berkeley, 130 Mulford Hall #3114, Berkeley, CA 94720, USA — ³Institute of Physics, Martin-Luther-University Halle-Wittenberg, 06099 Halle, Germany.

We investigate the Forest Fire Model in its version proposed by Henley (PRL 1993). Extracting the time series of shares of trees in the system, we investigate the temporal dynamics. For large tree growth probabilities p we find stable regions in which the system reaches a periodic attractor. With decreasing p the period of the attractor increments and for small values the system enters a chaotic regime as found in a Feigenbaum-Diagram. However, this chaotic regime also exhibits (quasi-)periodic fluctuations where the frequency is equal to p. On larger time-scales we observe a random walk behavior (≈ 1/f² scaling) which approaches white noise (approximately flat spectrum) for very long simulations, but 1/f noise only appears as a transition. The standard deviation of the fluctuations is proportional to p^1/2. Our results call for a new view on forest fire dynamics.