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A minimal model for self-organized critical percolation on directed graphs with activating and de-activating links is studied. Unlike classical self-organized criticality, the variables that determine criticality are separated from the…
I review the concept of self-organized criticality, wherein dissipative systems naturally drive themselves to a critical state with important phenomena occurring over a wide range of length and time scales. Several exact results are…
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.…
We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the…
We introduce a simple one-dimensional sandpile model that undergoes relaxation oscillations. A single model can account for self-organized critical behavior and relaxation oscillations, depending on the manner in which it is driven,…
It has long been argued that neural networks have to establish and maintain a certain intermediate level of activity in order to keep away from the regimes of chaos and silence. Strong evidence for criticality has been observed in terms of…
According to Pruessner and Peters [Phys. Rev. E {\bf 73}, 025106(R) (2006)], the finite size scaling exponents of the order parameter in sandpile models depend on the tuning of driving and dissipation rates with system size. We point out…
The Olami--Feder--Christensen earthquake model is often considered the prototype dissipative self--organized critical model. It is shown that the size distribution of events in this model results from a complex interplay of several…
We present a new model for relaxations in piles of granular material. The relaxations are determined by a stochastic rule which models the effect of friction between the grains. We find power-law distributions for avalanche sizes and…
We study extreme events of avalanche activities in finite-size two-dimensional self-organized critical (SOC) models, specifically the stochastic Manna model (SMM) and the Bak-Tang-Weisenfeld (BTW) sandpile model. Employing the approach of…
We present generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states. Using these scaling laws we present a collection of the…
We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical…
The dynamics of a fibre-bundle type model with equal load sharing rule is numerically studied. The system, formed by N elements, is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to…
A new quantity, average fitness, is introduced in Bak-Sneppen evolution model. Through this new quantity, a new hierarchy of avalanches is observed in the evolution of Bak-Sneppen model. An exact gap equation, governing the…
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…
A dissipative stochastic sandpile model is constructed and studied on small world networks in one and two dimensions with different shortcut densities $\phi$, where $\phi=0$ represents regular lattice and $\phi=1$ represents random network.…
Neural systems process information in a dynamical regime between silence and chaotic dynamics. This has lead to the criticality hypothesis which suggests that neural systems reach such a state by self-organizing towards the critical point…
We study a nonconservative sandpile model in one dimension, in which, if the height at any site exceeds a threshold value, the site topples by transferring one particle along each bond connecting it to its neighbours. Its height is then set…
We perform large-scale simulations of directed sandpile models with both deterministic and stochastic toppling rules. Our results show the existence of two distinct universality classes. We also provide numerical simulations of directed…
Motivated by recent experiments in neuroscience which indicate that neuronal avalanches exhibit scale invariant behavior similar to self-organized critical systems, we study the role of noisy (non-conservative) local dynamics on the…