Self-organized criticality in nonconservative mean-field sandpiles

A mean-field sandpile model that exhibits self-organized criticality (SOC) despite violation of the grain-transfer conservation law during avalanches is proposed. The sandpile consists of N agents and possesses background activity with intensity η ∈ [0, 1]. Background activity is characterized by transitions between two stable agent states. Analysis employing theories of branching processes and fixed points reveals a transition from sub-critical to SOC phase that is determined by ηN . The model is used to explain the school size distribution of free-swimming tuna as a result of population depletion. PACS. 05.65.+b Self-organized systems – 05.70.Fh Phase transitions: general studies – 89.75.Da Systems obeying scaling laws