# gst: self-organization to multicriticality; when a system can self-organize to a new type of phase transition while staying on the verge of another.

<< Self-organized criticality is a well-established phenomenon, where a system dynamically tunes its structure to operate on the verge of a phase transition. Here, (AA) show that the dynamics inside the self-organized critical state are fundamentally far more versatile than previously recognized, to the extent that a system can self-organize to a new type of phase transition while staying on the verge of another. >>

<< In this first demonstration of self-organization to multicriticality, (AA) investigate a model of coupled oscillators on a random network, where the network topology evolves in response to the oscillator dynamics. (They) 

 show that the system first self-organizes to the onset of oscillations, after which it drifts to the onset of pattern formation while still remaining at the onset of oscillations, thus becoming critical in two different ways at once. >>

 

<< The observed evolution to multicriticality is robust generic behavior that (AA) expect to be widespread in self-organizing systems. Overall, these results offer a unifying framework for studying systems, such as the brain, where multiple phase transitions may be relevant for proper functioning.>>

Silja Sormunen, Thilo Gross, Jari Saramäki. Self-organization to multicriticality. arXiv: 2506.04275v1 [nlin.AO]. Jun 4, 2025. 

https://arxiv.org/abs/2506.04275

Also: network, random, self-assembly, transition, brain, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, network, random, self-assembly, transition, phase transition, multiple phase transitions, self-organizing systems, self-organized criticality, multicriticality, brain.

# gst: an approach to delay solitary states within complex networks

AA << present a technique to engineer solitary states by means of delayed links in a network of neural oscillators and in coupled chaotic maps. Solitary states are intriguing partial synchronization patterns, where a synchronized cluster coexists with solitary nodes displaced from this cluster and distributed randomly over the network. >>

<< It is shown that the extent of displacement and the position of solitary elements can be completely controlled by the choice (values) and positions (locations) of the incorporated delays, reshaping the delay engineered solitary states in the network. >>

Leonhard Schulen, Saptarshi Ghosh, et al. Delay engineered solitary states in complex networks. arXiv:1908.01295v1 [nlin.AO] Aug 4, 2019.

https://arxiv.org/abs/1908.01295