# gst: discontinuous transition to chaos in a canonical random neural network

AA << study a paradigmatic random recurrent neural network introduced by Sompolinsky, Crisanti, and Sommers (SCS). In the infinite size limit, this system exhibits a direct transition from a homogeneous rest state to chaotic behavior, with the Lyapunov exponent gradually increasing from zero. (AA)  generalize the SCS model considering odd saturating nonlinear transfer functions, beyond the usual choice 𝜙⁡(𝑥)=tanh⁡𝑥. A discontinuous transition to chaos occurs whenever the slope of 𝜙 at 0 is a local minimum [i.e., for 𝜙′′′⁢(0)>0]. Chaos appears out of the blue, by an attractor-repeller fold. Accordingly, the Lyapunov exponent stays away from zero at the birth of chaos. >>

In the figure 7 << the pink square is located at the doubly degenerate point (𝑔,𝜀)=(1,1/3). >>️️

Diego Pazó. Discontinuous transition to chaos in a canonical random neural network. Phys. Rev. E 110, 014201. July 1, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.014201

Also: chaos, random, network, transition, neuro, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, random, network, transition, neuro

# gst: random walk model for dual cascades in wave turbulence.

<< Dual cascades in turbulent systems with two conserved quadratic quantities famously arise in both two-dimensional hydrodynamic turbulence and also in wave turbulence based on four-wave interactions. >>

<< in wave turbulence the systematic spectral fluxes observed in a dual cascade do not require an irreversible dynamical mechanism, rather, they arise as the inevitable outcome of blind chance. >>️️

Oliver Bühler. Random walk model for dual cascades in wave turbulence. Phys. Rev. E 109, 055102. May 1, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.055102

Also: waves, turbulence, random, weak, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, turbulence, weak turbulence, random, random walks

# gst: this arrangement may not be completely random; you might observe ordered structures (also) into amorphous (metallic glasses) solids

<< Glass, rubber and plastics all belong to a class of matter called amorphous solids. And in spite of how common they are in our everyday lives, amorphous solids have long posed a challenge to scientists. >>

A study << reports on the first-ever determination of the 3D atomic structure of an amorphous solid—in this case, a material called metallic glass. >>️

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<< Because amorphous solids have been so difficult to characterize, the researchers expected the atoms to be arranged chaotically. And although about 85% of the atoms were in a disordered arrangement, the researchers were able to identify pockets where a fraction of atoms coalesced into ordered superclusters. The finding demonstrated that even within an amorphous solid, the arrangement of atoms is not completely random. >>️

Wayne Lewis. Century-old problem solved with first-ever 3D atomic imaging of an amorphous solid. University of California, Los Angeles. Mar 31, 2021.

https://phys.org/news/2021-03-century-old-problem-first-ever-3d-atomic.html   

Yang Y., Zhou J., et al. Determining the three-dimensional atomic structure of an amorphous solid. Nature 592, 60–64.  doi: 10.1038/  s41586-021-03354-0. Mar 31, 2021.

https://www.nature.com/articles/s41586-021-03354-0    

# gst: near a critical point, switching between exploitation and exploration, to approach life with Lévy's (chaotic) walk

<< Lévy walks are common biological movements. However, the functional advantages of Lévy walks emerging near a critical point are poorly understood. >>

AA << showed that there could be functional advantages associated with Lévy walks emerging near a critical point, including a large dynamic range to stimuli and highly flexible switching between exploitation and exploration. >>

Masato S. Abe. Functional advantages of Lévy walks emerging near a critical point. PNAS.  doi: 10.1073/ pnas.2001548117.  Sep 14, 2020.

https://www.pnas.org/content/early/2020/09/11/2001548117

Chaotic 'Lévy walks' are a good strategy for animals. Riken. Sep 17, 2020.

https://phys.org/news/2020-09-chaotic-lvy-good-strategy-animals.html   

Also

Lévy flight hypothesis, not only for predation ...  Nov 22, 2015.

https://flashontrack.blogspot.com/2015/11/s-gst-levy-flight-hypothesis-not-only.html

keyword 'Lévy' in FonT

https://flashontrack.blogspot.com/search?q=L%C3%A9vy&m=1