Related papers: Forest Fire Model as a Supercritical Dynamic Model…
We review the properties of the self-organized critical (SOC) forest-fire model. The paradigm of self-organized criticality refers to the tendency of certain large dissipative systems to drive themselves into a critical state independent of…
We discuss the scaling behavior of the self-organized critical forest-fire model on large length scales. As indicated in earlier publications, the forest-fire model does not show conventional critical scaling, but has two qualitatively…
The scope of financial systemic risk research encompasses a wide range of interbank channels and effects, including asset correlation shocks, default contagion, illiquidity contagion, and asset fire sales. This paper introduces a financial…
We consider a forest-fire model which, somewhat informally, is described as follows: Each site (vertex) of the square lattice is either vacant or occupied by a tree.Vacant sites become occupied at rate 1. Further, each site is hit by…
Fire sales are among the major drivers of market instability in modern financial systems. Due to iterated distressed selling and the associated price impact, initial shocks to some institutions can be amplified dramatically through the…
Amongst the numerous models introduced with SOC, the Forest Fire Model (FFM) is particularly attractive for its close relationship to stochastic spreading, which is central to the study of systems as diverse as epidemics, rumours, or…
Critical infrastructure networks--including transportation, power grids, and communication systems--exhibit complex interdependencies that can lead to cascading failures with catastrophic consequences. These disasters often originate from…
We present a unified mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF)…
Depending on the rule for tree growth, the forest-fire model shows either self-organized criticality with rule-dependent exponents, or synchronization, or an intermediate behavior. This is shown analytically for the one-dimensional system,…
We investigate a forest-fire model with the density of empty sites as control parameter. The model exhibits three phases, separated by one first-order phase transition and one 'mixed' phase transition which shows critical behavior on only…
In this paper, we propose a dynamical model to capture cascading failures among interconnected organizations in the global financial system. Failures can take the form of bankruptcies, defaults, and other insolvencies. The network that…
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…
The 2008 financial crisis illustrated the need for a thorough, functional understanding of systemic risk in strongly interconnected financial structures. Dynamic processes on complex networks being intrinsically difficult, most recent…
Global catastrophic risk events, such as nuclear war, pose a severe threat to the stability of international financial systems. As evidenced by even less severe scenarios like the Great Recession, an economic failure can propagate through…
Since Self-Organised Criticality (SOC) was introduced in the 1987 both the nature of the self-organisation and of the criticality remains controversial. Recent observations on rain precipitation and on brain activity suggest that real…
``Self-Organised Criticality'' (SOC) is the mechanism by which complex systems spontaneously settle close to a *critical point*, at the edge between stability and chaos, and characterized by fat-tailed fluctuations and long-memory…
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:…
The existence of true scale-invariance in slowly driven models of self-organized criticality without a conservation law, as forest-fires or earthquake automata, is scrutinized in this paper. By using three different levels of description -…
As impressively shown by the financial crisis in 2007/08, contagion effects in financial networks harbor a great threat for the stability of the entire system. Without sufficient capital requirements for banks and other financial…
The latest financial crisis has painfully revealed the dangers arising from a globally interconnected financial system. Conventional approaches based on the notion of the existence of equilibrium and those which rely on statistical…