Related papers: Self-Organized Criticality and Synchronization in …
The forest fire model is a reaction-diffusion model where energy, in the form of trees, is injected uniformly, and burned (dissipated) locally. We show that the spatial distribution of fires forms a novel geometric structure where the…
Self-organized criticality is a well-established phenomenon, where a system dynamically tunes its structure to operate on the verge of a phase transition. Here, we show that the dynamics inside the self-organized critical state are…
We re-examine a two-dimensional forest-fire model via Monte-Carlo simulations and show the existence of two length scales with different critical exponents associated with clusters and with the usual two-point correlation function of trees.…
Fires and rainfall are major mechanisms that regulate woody and grassy biomasses in savanna ecosystems. Conditions of long-lasting coexistence of trees and grasses have been mainly studied using continuous-time modelling of tree-grass…
We investigate a suggested path to self-organized criticality. Originally, this path was devised to "generate criticality" in systems displaying an absorbing-state phase transition, but closer examination of the mechanism reveals that it…
We reconsider a model introduced by Bak, Chen, and Tang (Phys. Rev. A 38, 364 (1988)) as a supposedly self-organized critical model for forest fires. We verify again that the model is not critical in 2 dimensions, as found also by previous…
The disorder and a simple convex measure of complexity are studied for rank ordered power law distributions, indicative of criticality, in the case where the total number of ranks is large. It is found that a power law distribution may…
Self-organized criticality elucidates the conditions under which physical and biological systems tune themselves to the edge of a second-order phase transition, with scale invariance. Motivated by the empirical observation of bimodal…
Many natural phenomena exhibit power law behaviour in the distribution of event size. This scaling is successfully reproduced by Self Organized Criticality (SOC). On the other hand, temporal occurrence in SOC models has a Poisson-like…
Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…
Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For…
A new type of spatial-temporal correlation in the process approaching to the self-organized criticality is investigated for the two simple models for biological evolution. The change behaviors of the position with minimum barrier are shown…
We present a general conceptual framework for self-organized criticality (SOC), based on the recognition that it is nothing but the expression, ''unfolded'' in a suitable parameter space, of an underlying {\em unstable} dynamical critical…
We prove the well-posedness of a differential equation that describes the evolution of the large-system limit of the empirical age measure in the mean field forest fire model of R\'ath and T\'oth (arXiv:0808.2116). This forest fire model is…
The presence of both critical behavior and oscillating patterns in brain dynamics is a very interesting issue. In this paper, we consider a model for a neuron population, where each neuron is modeled by an over-damped rotator. We find that…
Prescribed burns have been increasingly utilized in forest management in the past few decades. However, their effectiveness in reducing the risk of destructive wildfires has been debated. The sandpile model of self-organized criticality,…
Tree-grass coexistence in savanna ecosystems depends strongly on environmental disturbances out of which crucial is fire. Most modeling attempts in the literature lack stochastic approach to fire occurrences which is essential to reflect…
The self-organized critical state is characterized by a power law distribution of cluster sizes and other properties. However experiments with sand and rice piles reveal distributions of avalanche sizes which are not power law distributed.…
Since Self-Organised Criticality (SOC) was introduced in 1987, both the nature of the self-organisation and the criticality remains controversial. Recent observations on rain precipitation and brain activity suggest that real systems…
We propose a discrete two-dimensional mathematical model for forest fires and we derive certain results describing its limiting behavior. We also pose a relevant open question.