Self-organisation of living systems towards criticality at the edge of chaos.

A principle of self-organization toward a critical state is proposed as a metadynamics of evolutionary processes. When the propagation velocity of information is slow as in living systems, discrepancy occurs between the virtual process and the actual one. The degree of discrepancy is defined for discrete dynamical systems on the scheme of perpetual disequilibration (PD), proposed by Gunji and others. It is supposed that adaptable systems tend to evolve so that the discrepancy may be minimized. A principle of the minimum degree of PD is applied to cellular automata and Boolean networks. These complex systems have the minimum degree of PD at the border between order and chaos, and thus are expected to evolve to the critical state at the edge of chaos. This self-organized criticality is a generalized form of Bak's self-organized criticality.