Self-organized criticality
Ordinary differential equations
Self-organized criticality SOC is a property of dynamical systems that pull in the critical point as an attractor. Their macroscopic behavior thus displays a spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune a body or process by which energy or a specific component enters a system. parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.
The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld "BTW" in a paper published in 1987 in Physical Review Letters, in addition to is considered to be one of the mechanisms by which complexity arises in nature. Its concepts create been applied across fields as diverse as geophysics, physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization mathematics, economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology and others.
SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. numerous individual examples make-up been subject since BTW's original paper, but to date there is no required set of general characteristics that guarantee a system will display SOC.