Related papers: Forest-fire models as a bridge between different p…

We discuss the properties of a self--organized critical forest--fire model which has been introduced recently. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer…

We show that deterministic systems with strong nonlinearities seem to be more appropriate to model sandpiles than stochastic systems or deterministic systems in which discontinuities are the only nonlinearity. In particular, we are able to…

We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the…

Savannas are characterized by a discontinuous tree layer superimposed on a continuous layer of grass. Identifying the mechanisms that facilitate this tree-grass coexistence has remained a persistent challenge in ecology and is known as the…

We introduce a deterministic self-organized critical system that is one dimensional and bulk driven. We find that there is no universality class associated with the system. That is, the critical exponents change as the parameters of the…

Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of…

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…

We investigate the scaling behavior of the cluster size distribution in the Drossel-Schwabl Forest Fire model (DS-FFM) by means of large scale numerical simulations, partly on (massively) parallel machines. It turns out that simple scaling…

We introduce a novel approach to study the critical behavior of equilibrium and non-equilibrium systems which is based on the concept of an instantaneous correlation length. We analyze in detail two classical statistical mechanical systems:…

We study finite-size effects in the self-organized critical forest-fire model by numerically evaluating the tree density and the fire size distribution. The results show that this model does not display the finite-size scaling seen in…

We present the analytic solution of the self-organized critical (SOC) forest-fire model in one dimension proving SOC in systems without conservation laws by analytic means. Under the condition that the system is in the steady state and very…

Forest-savanna bistability - the hypothesis that forests and savannas exist as alternative stable states in the tropics - and its implications are key challenges for mathematical modelers and ecologists in the context of ongoing climate…

Rotational constraint representing a local external bias generally has non-trivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in a out of…

We present the first solvable non-conservative sandpile-like critical model of Self-Organized Criticality (SOC), and thereby substantiate the suggestion by Vespignani and Zapperi [A. Vespignani and S. Zapperi, Phys. Rev. E 57, 6345 (1998)]…

Both the deterministic and stochastic sandpile models are studied on the percolation backbone, a random fractal, generated on a square lattice in $2$-dimensions. In spite of the underline random structure of the backbone, the deterministic…

In this paper we use a variant of the Watts-Strogatz small-world model to predict wildfire behavior near the critical propagation/nonpropagation threshold. We find that forest fire patterns are fractal and that critical exponents are…

Models for wildfires must be stochastic if their ability to represent wildfires is to be objectively assessed. The need for models to be stochastic emerges naturally from the physics of the fire, and methods for assessing fit are…

We introduce two sandpile models which show the same behavior of real sandpiles, that is, an almost self-organized critical behavior for small systems and the dominance of large avalanches as the system size increases. The systems become…

In this thesis we present few theoretical studies of the models of self-organized criticality. Following a brief introduction of self-organized criticality, we discuss three main problems. The first problem is about growing patterns formed…

We present results on a stochastic forest fire model, where the influence of the neighbour trees is treated in a more realistic way than usual and the definition of neighbourhood can be tuned by an additional parameter. This model exhibits…