Controlled bio-inspired self-organised criticality

Abstract

AbstractThe control of extensive complex biological systems is considered to depend on 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. 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 with 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 is 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, remote consumers of biological resources, with globally defined control.Author summaryUsing a nonlinear control method inspired by enzymatic control, which is capable of stabilising chaotic systems into periodic orbits or steady-states, it is shown that a controlled system can be created that is scale-free and in a critical state. This means that the system can easily move from one stable orbit to another using only a small local perturbation. Such a system is known as self-organised criticality, and is shown in this system to be deterministic. Using a known perturbation, it will result in a scale-free response of the system that can be in a power law relation. It has been conjectured that biosystems are in a self-organised critical state, and these models show that this is a suitable approach to allow local systems to control a global state, such as homeostatic control. The underlying principle is based on rate control of chaos, and can be used to understand how biosystems can use localised control to ensure stability at different dynamic scales without supervising mechanisms.