Self-organized (quasi-)criticality: the extremal Feder and Feder model

TL;DR

This paper introduces a simple SOC model combining features of Bak-Sneppen and slip-stick models, providing analytical insights into avalanche sizes and state distributions in dissipative systems.

Contribution

It presents a new random-neighbor SOC model with an analytical approach to avalanche dynamics and state distributions, bridging properties of existing models.

Findings

Mean avalanche size is exactly calculable as a function of coupling strength.

State distribution in the thermodynamic limit has a simple analytical form.

The model offers transparent insights into large avalanche development in dissipative systems.

Abstract

A simple random-neighbor SOC model that combines properties of the Bak-Sneppen and the relaxation oscillators (slip-stick) models is introduced. The analysis in terms of branching processes is transparent and gives insight about the development of large but finite mean avalanche sizes in dissipative models. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter strength, is exactly calculable.