Self-Organised Criticality Equation Files

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.

复杂生物系统被认为是通过反馈机制进行调控的。简化系统建模曾有效描述此类调控机制，但该方法未能充分涵盖理解"生物系统中的局域控制如何产生全局稳定态"所需的复杂程度。自组织临界性（Self-Organised Criticality, SOC）是局域相互作用物理系统的一类特征属性，这类系统会因小型非线性微扰引发动态状态变化，进而自发涌现出SOC特性。局域状态或局域相互作用中的微小变化，可对临界系统的整体系统状态产生显著影响。长期以来，学界推测SOC是生物系统的核心属性：生物系统不仅展现出类似的临界动力学特性，还可能呈现近似幂律关系。混沌速率控制（Rate Control of Chaos, RCC）提供了一种适用于生成SOC系统的鲁棒机制，该机制运行于混沌边缘。这种仿生RCC方法仅需获取系统部分变量的局域瞬时信息，便可适配局域微扰。值得注意的是，经RCC调控的互联振子网络能够维持全局多稳态，且可形成可能涌现幂律关系的区域。该振子网络可确定性地稳定至对应不同微扰的不同轨道，且微扰与振幅间的关联可呈现指数关联与幂律关联。这一过程可被视为蛋白质生产与调控这一基础机制的表征，而该机制是稳态平衡等复杂生命过程的基础。通过引入来自全局状态的反馈，可增强或抑制整体系统的动态行为。受控SOC可大幅提升我们对生物调控机制的理解：这类机制基于分布式局域产生单元、远端生物资源消费单元以及全局定义的调控方式构建。