# gst: the hypothesis of the onset of extreme events via an attractor merging crisis.

AA << investigate the temporal dynamics of the Ikeda Map with Balanced Gain and Loss and in the presence of feedback loops with saturation nonlinearity. From the bifurcation analysis, (They) find that the temporal evolution of optical power undergoes period quadrupling at the exceptional point (EP) of the system and beyond that, chaotic dynamics emerge in the system and this has been further corroborated from the Largest Lyapunov Exponent (LLE) of the model. >>

<< For a closer inspection, (AA) analyzed the parameter basin of the system, which further leads to (their) inference that the Ikeda Map with Balanced Gain and Loss exhibits the emergence of chaotic dynamics beyond the exceptional point (EP). >>

<< Furthermore, (AA) find that the temporal dynamics beyond the EP regime leads to the onset of Extreme Events (EE) in this system via attractor merging crisis. >>️

Jyoti Prasad Deka, Amarendra K. Sarma. Temporal Dynamics beyond the Exceptional Point in the Ikeda Map with Balanced Gain and Loss. arXiv: 2406.17783 [eess.SP]. May 13, 2024. 

https://arxiv.org/abs/2406.17783 

Also: chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, chaotic dynamics, attractor merging crisis 

# gst: the effect of noise on the dynamics of microswimmers in externally-driven fluid flows.

AA << have quantified the effect of noise on swimmer dynamics in a steady, two-dimensional hyperbolic fluid flow. In such a flow, swimmers are ultimately forced to escape to the left or the right, with their transient dynamics near the passive unstable fixed point determining which way they go. >>

<< Without noise, a swimmer’s fate is sealed based on its position relative to the SwIM (swimming invariant manifolds) in the xθ phase space. With noise, the swimmer’s motion is a stochastic process. >>

AA << calculated the steady-state orientation distributions of diffusive, run-and-tumble, or mixed swimmers in the hyperbolic flow. The fluctuations give some swimmers greater opportunity to cross the SwIM and exit on the opposite side than they would have without noise. There is however a maximal distance that swimmers can get on either side of the passive fixed point and still be able to swim back to the other side—this is where the stable BIMs (burning invariant manifolds) block inward swimming particles. >>

<< Fluctuations make it increasingly likely that a swimmer close to one of these BIMs does indeed end up crossing it, causing irreversible changes to the fluctuating swimmers’ trajectories (assuming negligible translational diffusion).  >>️

Simon A. Berman, Kevin A. Mitchell. Swimmer dynamics in externally-driven fluid flows: The role of noise. arXiv: 2108.10488v1 [physics.flu-dyn]. Aug 24, 2021.

https://arxiv.org/abs/2108.10488

keywords: gst, swimmer, swimming particle, fluid dynamics, chaotic dynamics, rotational diffusion, random fluctuation, tumbling, noise

# gst: chaotic dynamics modulate complex systems, even in the presence of extrinsic and intrinsic noise

AA << find that chaotic dynamics modulates gene expression and up-regulates certain families of low-affinity genes, even in the presence of extrinsic and intrinsic noise. Furthermore, this leads to an increase in the production of protein complexes and the efficiency of their assembly. Finally, (AA) show how chaotic dynamics creates a heterogeneous population of cell states, and describe how this can be beneficial in multi-toxic environments. >>

Mathias L. Heltberg, Sandeep Krishna, Mogens H. Jensen. On chaotic dynamics in transcription factors and the associated effects in differential gene regulation.  Nature Comm. volume 10, Article number: 71 Jan 8, 2019.   https://www.nature.com/articles/s41467-018-07932-1  

<< Chaos in bodily regulation can optimize our immune system according to a recent discovery made by researchers at the University of Copenhagen's Niels Bohr Institute. The discovery may prove to be of great significance for avoiding serious diseases such as cancer and diabetes.  >>

Chaos in the body tunes up your immune system. Niels Bohr Institute.
Jan 16, 2019.   https://m.medicalxpress.com/news/2019-01-chaos-body-tunes-immune.html

Also

'l'immaginifico "tracciante ... che svagola nella macina ...'    in:  2149 - onda di predazione (to knock seals off the ice). Notes. Dec 17, 2007.    https://inkpi.blogspot.com/2007/12/2149-onda-di-predazione-to-knock-seals.html

Also

never boring with chaos and tit-for-tat theories. F.on.T. Jun 12, 2016.  https://flashontrack.blogspot.com/2016/06/s-gst-never-boring-with-chaos-and-tit.html

# gst: apropos to try numerically to discover states with desired response properties in chaotic (i.e. normal - ab.normal) systems, by Hridesh, Deng, Jean-Jacques, Jeremy.

  <<
Systems with many stable configurations abound in nature, both in living and inanimate matter. Their inherent nonlinearity and sensitivity to small perturbations make them challenging to study, particularly in the presence of external driving, which can alter the relative stability of different attractors. Under such circumstances, one may ask whether any clear relationship holds between the specific pattern of external driving and the particular attractor states selected by a driven multistable system. To gain insight into this question, (AA)  numerically study driven disordered mechanical networks of bistable springs which possess a vast number of stable configurations arising from the two stable rest lengths of each spring, thereby capturing the essential physical properties of a broad class of multistable systems.  (AA) find that the attractor states of driven disordered multistable mechanical networks are fine-tuned with respect to the pattern of external forcing to have low work absorption from it. Furthermore,  (AA)  find that these drive-specific attractor states are even more stable than expected for a given level of work absorption.  (AA)  results suggest that the driven exploration of the vast configuration space of these systems is biased towards states with exceptional relationship to the driving environment, and could therefore be used to 'discover' states with desired response properties in systems with a vast landscape of diverse configurations.
  >>

Hridesh Kedia, Deng Pan, et al. Drive-specific adaptation in disordered mechanical networks of bistable springs. arXiv:1908.09332v1 [nlin.AO] Aug 25, 2019.    https://arxiv.org/abs/1908.09332 

Also

keyword "three" in: FonT    https://flashontrack.blogspot.com/search?q=three

keyword "three" in: Notes      https://inkpi.blogspot.com/search?q=three

# 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