Self-organised criticality models

Complex biological systems are considered to be controlled using feedback
mechanisms. Reduced systems modelling has been effective to describe these
mechanisms, but this approach does not sufficiently encompass the
required complexity that is needed to understand how localised
control in a biological system can provide global stable states.
Self-Organised Criticality (SOC) is a characteristic property of locally
interacting physical systems, which readily emerges from changes to its
dynamic state due to small nonlinear perturbations. These small changes in
the local states, or in local interactions, can greatly affect the total
system state of critical systems. It has long been conjectured that SOC is
cardinal to biological systems, that show similar critical dynamics, and
also may exhibit near power-law relations. Rate Control of Chaos (RCC)
provides a suitable robust mechanism to generate SOC systems, which
operates at the edge of chaos. The bio-inspired RCC method requires only
local instantaneous knowledge of some of the variables of the system, and
is capable of adapting to local perturbations. Importantly, connected RCC
controlled oscillators can maintain global multi-stable states, and
domains where power-law relations may emerge. The network of oscillators
deterministically stabilises into different orbits for different
perturbations, and the relation between the perturbation and amplitude can
show exponential and power-law correlations. This can be considered to be
representative of a basic mechanism of protein production and control,
that underlies complex processes such as homeostasis. Providing feedback
from the global state, the total system dynamic behaviour can be boosted
or reduced. Controlled SOC can provide much greater understanding of
biological control mechanisms, that are based on distributed local
producers, with remote consumers of biological resources, and globally
defined control.