Self-organization with memory.

Highlights • Distinctive features of self-organization with memory are described. • Appearance of memory in process can generate a self-organization. • Principles of self-organization my power-law memory are suggested. • Change of memory fading can lead to significant change of characteristic times. • Generalization of method of adiabatic elimination of fast variables is proposed. Abstract In this paper we propose a generalization of method of adiabatic elimination of fast relaxing variables, which is a special form of the slaving principle, to the case of processes with power-law memory. Simple models to describe the distinctive features of the self-organized processes with power-law memory are considered. We have proved that when the memory fading parameters change, the processes with memory can significantly change its rates (by many orders of magnitude) and change the characteristic times both upward and downward. Therefore the parameters of memory fading can be considered as control parameters that change of characteristic time of processes. Some principles to describe specific features of self-organization with memory are proposed. [ABSTRACT FROM AUTHOR]