Editing Chaos theory (section)

==Spontaneous order==
Under the right conditions, chaos spontaneously evolves into a lockstep pattern. In the [[Kuramoto model]], four conditions suffice to produce synchronization in a chaotic system.
Examples include the [[coupled oscillation]] of [[Christiaan Huygens]]' pendulums, fireflies, [[neuron]]s, the [[London Millennium Bridge]] resonance, and large arrays of [[Josephson junctions]].<ref>Steven Strogatz, ''Sync: The Emerging Science of Spontaneous Order'', Hyperion, 2003.</ref>

Moreover, from the theoretical physics standpoint, dynamical chaos itself, in its most general manifestation, is a spontaneous order. The essence here is that most orders in nature arise from the [[Spontaneous symmetry breaking|spontaneous breakdown]] of various symmetries. This large family of phenomena includes elasticity, superconductivity, ferromagnetism, and many others. According to the [[supersymmetric theory of stochastic dynamics]], chaos, or more precisely, its stochastic generalization, is also part of this family. The corresponding symmetry being broken is the [[Topological quantum field theory|topological supersymmetry]] which is hidden in all [[Stochastic differential equation|stochastic (partial) differential equations]], and the corresponding [[Phase transition|order parameter]] is a [[Quantum field theory|field-theoretic]] embodiment of the butterfly effect.<ref>{{Cite journal |last=Ovchinnikov |first=I.V. |title=Ubiquitous order known as chaos |date=2024-02-15 |journal=Chaos, Solitons & Fractals |language=en |volume=181 |issue=5 |pages=114611 |doi=10.1016/j.chaos.2024.114611 |arxiv=2503.17157 |bibcode=2024CSF...18114611O |url=https://www.sciencedirect.com/science/article/abs/pii/S0960077924001620 |issn = 0960-0779}}</ref>