Related papers: Self-organization without conservation: true or ju…
It is a common belief that power-law distributed avalanches are inherently unpredictable. This idea affects phenomena as diverse as evolution, earthquakes, superconducting vortices, stock markets, etc; from atomic to social scales. It…
Self-organized criticality is characterized by power law correlations in the non-equilibrium steady state of externally driven systems. A dynamical system proposed here self-organizes itself to a critical state with no characteristic size…
Scale-invariant avalanches -- with events of all sizes following power-law distributions -- are considered critical. Above the upper critical dimension of four, the mean-field solution with a robust $3/2$ size exponent describes the…
The idea that information-processing systems operate near criticality to enhance computational performance is supported by scaling signatures in brain activity. However, external signals raise the question of whether this behavior is…
Self-organized criticality (SOC) is widely proposed as a fundamental mechanism for collective behavior, yet its role in objective-driven, heterogeneous adaptive systems underpinning real complex systems remains less understood. We introduce…
Discrete scale invariance, which corresponds to a partial breaking of the scaling symmetry, is reflected in the existence of a hierarchy of characteristic scales l0, c l0, c^2 l0,... where c is a preferred scaling ratio and l0 a microscopic…
We explore the connection between self-organized criticality and phase transitions in models with absorbing states. Sandpile models are found to exhibit criticality only when a pair of relevant parameters - dissipation epsilon and driving…
The dynamics based on information transfer is proposed as an underlying mechanism for the scale-invariant dynamic critical behavior observed in a variety of systems. We apply the dynamics to the globally-coupled Ising model, which is…
``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…
The unreduced, universally nonperturbative analysis of arbitrary many-body interaction process reveals the irreducible, purely dynamic source of randomness. It leads to the universal definition of real system complexity (physics/9806002),…
Power laws in nature are considered to be signatures of complexity. The theory of self-organized criticality (SOC) was proposed to explain their origins. A longstanding principle of SOC is the \emph{separation of timescales} axiom. It…
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:…
Neural systems face the challenge of maintaining reliable representations amid variations from plasticity and spontaneous activity. In particular, the spontaneous dynamics in neuronal circuit is known to operate near a highly variable…
In all local low-dimensional models, scaling at critical points deviates from mean field behavior -- with one possible exception. This exceptional model with ``ordinary" behavior is an inherently non-equilibrium model studied some time ago…
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…
We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically…
The Drossel-Schwabl Forest Fire Model is one of the best studied models of non-conservative self-organised criticality. However, using a new algorithm, which allows us to study the model on large statistical and spatial scales, it has been…
We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general…
Local scale invariance (LSI) has been recently proposed as a possible extension of the dynamical scaling in systems at the critical point and during phase ordering. LSI has been applied inter alia to provide predictions for the scaling…
We numerically investigate the Olami-Feder-Christensen model for earthquakes in order to characterise its scaling behaviour. We show that ordinary finite size scaling in the model is violated due to global, system wide events. Nevertheless…