# gst: evolving disorder and chaos induces acceleration of elastic waves.

<< Static or frozen disorder, characterised by spatial heterogeneities, influences diverse complex systems, encompassing many-body systems, equilibrium and nonequilibrium states of matter, intricate network topologies, biological systems, and wave-matter interactions. >>

AA << investigate elastic wave propagation in a one-dimensional heterogeneous medium with diagonal disorder. (They) examine two types of complex elastic materials: one with static disorder, where mass density randomly varies in space, and the other with evolving disorder, featuring random variations in both space and time. (AA) results indicate that evolving disorder enhances the propagation speed of Gaussian pulses compared to static disorder. Additionally, (They) demonstrate that the acceleration effect also occurs when the medium evolves chaotically rather than randomly over time. The latter establishes that evolving randomness is not a unique prerequisite for observing wavefront acceleration, introducing the concept of chaotic acceleration in complex media. >>️

M. Ahumada, L. Trujillo, J. F. Marín. Evolving disorder and chaos induces acceleration of elastic waves. arXiv: 2403.02113v1 [cond-mat.dis-nn]. Mar 4, 2024. 

https://arxiv.org/abs/2403.02113

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

Keywords: gst, waves, elastic, chaos, transition

# gst: near the Hopf boundary, Intermittency and chimera states.

AA << study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. >>️

<< For analysis, (AA) first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors. Consequently, different oscillators may show a dynamics that is intermittently synchronized (or desynchronized), giving rise to intermittent chimera states. The behavior of the intermittent laminar phases is characterized by the characteristic time spent in the synchronization manifold, which decays as a power law. >>

<< Such intermittent dynamics is quite general and is also observed in an ensemble of a large number of oscillators arranged in variety of network topologies including nonlocal, scale-free, random, and small-world networks. >>️

Anjuman Ara Khatun, Yusra Ahmed Muthanna, et al. Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states. Phys. Rev. E 109, 034208. March 15, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.034208

Also: transition, intermittency, chaos, chimera, network, in https://www.inkgmr.net/kwrds.html

Keywords: gst, transition, intermittency, chaos, chimera, network

gst: actually and counterintuitively a coherent jump could generate disorder.

AA << consider a quantized version of a model for “random walk in random environment.” (..) For a ring geometry (a chain with periodic boundary condition) it features a delocalization-transition as the bias in increased beyond a critical value, indicating that the relaxation becomes underdamped. Counterintuitively, the effective disorder is enhanced due to coherent hopping. >>

Ben Avnit, Doron Cohen. Quantum walk in stochastic environment. Phys. Rev. E 108, 054111. Nov 7, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.054111

Also:  Voli a casaccio. Notes (quasi-stochastic poetry). Oct 01, 2006.

https://inkpi.blogspot.com/2006/10/2066-voli-casaccio.html

Also: 'random', 'transition', 'disorder', 'chaos', in https://www.inkgmr.net/kwrds.html

Keywords: gst, walk, random walk, quantum walk, qu-walk, jump, transition, disorder, chaos

# gst: apropos of transitions, three distinct new families of long-wave instabilities and potential new pathways to turbulence.

AA << reveal three previously unknown instabilities, distinct from the well-known Kelvin-Helmholtz Instability (KHI) and Holmboe Wave Instability (HWI), in that they have longer wavelengths (..) and often slower growth rates. >>

<< The circumstances under which turbulence can persist in strongly stratified flows remains a fascinating debate within the community. [AA] demonstrated that weakly unstable (very) long waves may trigger turbulence and mixing after long periods of time, even under initially very strongly stratified conditions. >>

Lu Zhu, Amir Atoufi, Adrien Lefauve, Rich R. Kerswell, P. F. Linden. Long-wave instabilities of sloping stratified exchange flows. arXiv:2309.10056v1 [physics.flu-dyn]. Sep 18, 2023.

https://doi.org/10.48550/arXiv.2309.10056

Also: waves, instability, transition, turbulence, chaos, in https://www.inkgmr.net/kwrds.html

Keywords: gst, waves, instability, long-wave instability, transition, turbulence, chaos

# gst: chimera resonance, in analogy with the effects of stochastic and coherence resonance

AA << explore numerically the impact of additive Gaussian noise on the spatio-temporal dynamics of ring networks of nonlocally coupled chaotic maps. >>

️

<<  It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. >>

<< This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance. >>️

Elena Rybalova, Vasilii Nechaev, Eckehard Schöll, Galina Strelkova. Chimera resonance in networks of chaotic maps. arXiv:2307.00006v2 [cond-mat.dis-nn]. Jul 5, 2023.

https://arxiv.org/abs/2307.00006

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

Keywords: gst, chimera, noise, chaos, network, chimera resonance

# gst: sudden phase transitions among nonconservative system with nonreciprocal interactions

<< A nonconservative system with nonreciprocal interaction has been found to reveal exotic features where sudden phase transitions can occur. >>️

Here AA reported << the emanation of a chimera in a network of Stuart-Landau oscillators. >>

<< The findings could have pragmatic implications in the areas of active matter, networks, and photonics. >>

️

M. Paul Asir. Emergence of chimeras: An impetus by exceptional points. Phys. Rev. E 108, 024220. Aug 22, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.024220

Also: Stuart–Landau equation. 

https://en.m.wikipedia.org/wiki/Stuart%E2%80%93Landau_equation

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

Keywords: network, transition, chimera, chaos, pattern formation

# gst: transitions by coupled instabilities

AA << present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. (They)  show that the transition is driven initially by a long-wave amplitude modulation instability, which excites the oscillatory transition phase instability, leading to the formation of dislocations in the Faraday lattice. The appearance of dislocations dampens amplitude modulations, which prevents further defects from being created and allows the system to relax back to its ordered state. The process then repeats itself in a quasiperiodic manner. >>

Valeri Frumkin, Shreyas Gokhale. Coupled instabilities drive quasiperiodic order-disorder transitions in Faraday waves. Phys. Rev. E 108, L012601. July 17, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.L012601

Also: parrondo, tit-for-tat, game, transition, chaos, in https://www.inkgmr.net/kwrds.html

Keywords: parrondo, tit-for-tat, game,  transition, chaos

# gst: apropos of coexistence of coherent and incoherent oscillators, chaotic chimera attractors in a triangular network.

<< A prominent type of collective dynamics in networks of coupled oscillators is the coexistence of coherently and incoherently oscillating domains known as chimera states. >>️

<< In a three-population network of identical Kuramoto-Sakaguchi phase oscillators, stationary and periodic symmetric chimeras were previously studied on a reduced manifold in which two populations behaved identically. >>

<< In this paper, (AA) study the full phase space dynamics of such three-population networks. (They) demonstrate the existence of macroscopic chaotic chimera attractors that exhibit aperiodic antiphase dynamics of the order parameters. >>

<< The chaotic chimera states coexist with a stable chimera solution on the Ott-Antonsen manifold that displays periodic antiphase oscillation of the two incoherent populations and with a symmetric stationary chimera solution, resulting in tristability of chimera states. Of these three coexisting chimera states, only the symmetric stationary chimera solution exists in the symmetry-reduced manifold. >>️

Seungjae Lee, Katharina Krischer. Chaotic chimera attractors in a triangular network of identical oscillators. Phys. Rev. E 107, 054205. May 8, 2023.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.107.054205

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

Keywwords: gst, chimera, bifurcations, chaos, synchronization

# gst: apropos of transitions, a perpetual dance between states of meta-stability and chaos (in brain).

img: https://wp.technologyreview.com/wp-content/uploads/2023/02/Radio_image_15.jpeg?fit=2160,1214

<< Hello! Today: new research is shining a light on how our brains flit between states of stability and chaos, depending on what we’re doing. >>

<< Our brains exist in a state somewhere between stability and chaos as they help us make sense of the world, according to recordings of brain activity taken from volunteers over the course of a week. >>

<< As we go from reading a book to chatting with a friend, for example, our brains shift from one semi-stable state to another—but only after chaotically zipping through multiple other states in a pattern that looks completely random. >>

<< Understanding how our brains restore some degree of stability after chaos could help us work out how to treat disorders at either end of this spectrum. Too much chaos is probably what happens when a person has a seizure, whereas too much stability might leave a person comatose. >>

Jessica Hamzelou. Neuroscientists listened in on people’s brains for a week. They found order and chaos. Rhiannon Williams. MIT Download. Feb 8, 2023.

https://mailchi.mp/technologyreview.com/mass-market-military-drones-have-changed-the-way-wars-are-fought-839014

<< The team (Avniel Ghuman, Maxwell Wang, et al.) found some surprising patterns in brain activity over the course of the week. Specific brain networks seemed to communicate with each other in what looked like a “dance,” with one region appearing to “listen” while the other “spoke,” say the researchers, who presented their findings at the Society for Neuroscience annual meeting in San Diego last year. >>

Jessica Hamzelou. MIT Tech Rev. Feb 7, 2023. 

https://www.technologyreview.com/2023/02/07/1067951/brains-week-order-chaos

Also 

keyword 'danza' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=danza

keyword 'dance' in FonT

https://flashontrack.blogspot.com/search?q=dance

keyword 'cervello' | 'brain' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=cervello

https://inkpi.blogspot.com/search?q=brain

keyword 'brain' in FonT

https://flashontrack.blogspot.com/search?q=brain

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

<< Amico, qualunque  cosa suonerai . . . >>  Jelly Roll Morton. cit.: 2113 - soniche a ramulo. Jan 28, 2007

http://inkpi.blogspot.it/2007/01/2113-soniche-ramulo.html

https://inkpi.blogspot.com/search?q=jelly+roll

Keywords: gst, brain, transition, chaos, dance

# gst: transitions, how two saddles can increase the transient times.

FIG. 8. Attractor and chaotic saddles (..) amplified around three bands of the chaotic attractor.  The global chaotic saddle is colored blue, and the local chaotic saddle is colored red. The attractors are colored black. 

AA << consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems, they are responsible for chaotic transients, fractal basin boundaries, chaotic scattering and they mediate interior crises. >>

<< In this work (AA) discuss the creation of chaotic saddles in a dissipative nontwist system and the interior crises they generate. (They) show how the presence of two saddles increase the transient times and analyze the phenomenon of crisis induced intermittency. >>️

Rodrigo Simile Baroni, Ricardo Egydio de Carvalho, et al. Chaotic saddles and interior crises in a dissipative nontwist system. arXiv: 2211.06921v1 [nlin.CD]. Nov 13, 2022. 

https://arxiv.org/abs/2211.06921

Also

keyword 'intermittency' in FonT

https://flashontrack.blogspot.com/search?q=intermittency

keyword 'dissipation' in FonT

https://flashontrack.blogspot.com/search?q=dissipation

keyword 'saddle' in FonT

https://flashontrack.blogspot.com/search?q=saddle

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

Keywords: gst, transitions, dissipation, 

dissipative systems, chaos, saddle, chaotic saddle, crisis, interior crisis, intermittency

# gst: apropos of vibrating pivots, driving a damped coplanar double pendulum.

AA << present results of linear and nonlinear motions of a parametrically driven coplanar double pendulum with velocity-dependent damping. The equations of motion of a damped double pendulum of unequal masses with its pivot vibrated vertically are different from those obtained under gravity modulation. 

Linear stability analysis shows that tongue-shaped marginal stability curves divide the plane of driving parameters into multiple regions of subharmonic and harmonic instabilities. The instability zones for one normal mode overlap with those for the other. 

The double pendulum may oscillate or rotate about its pivot harmonically or subharmonically. The limit cycles corresponding to the normal mode oscillations of a double pendulum of equal masses are squeezed into a line in its configuration space. 

For unequal masses, two marginal curves for subharmonic instabilities merge to form a double-well shaped curve in the presence of damping, which is qualitatively new. The pendulum shows driving amplitude sensitive multi-period complex oscillations for driving parameters near the extrema of the merged instability zones and boundaries of the overlapping zones. 

For larger driving amplitude, the pendulum shows subharmonic, harmonic or chaotic rotations. >>

️

Rebeka Sarkar, Krishna Kumar, Sugata Pratik Khastgir. Parametrically driven damped coplanar double pendulum. arXiv:2208.03292v1 [physics.class-ph]. Aug 2, 2022. 

https://arxiv.org/abs/2208.03292

Also

keyword 'pendulum' in FonT

https://flashontrack.blogspot.com/search?q=pendulum

keyword 'pendolo' | 'pendola' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=pendolo

https://inkpi.blogspot.com/search?q=pendola

Keywords: gst, pendulum, double pendulum, instability, chaos, chaotic rotations

# gst: how a synchronization could emerge from chaotic activities

<< Can we find order in chaos? Physicists have shown, for the first time that chaotic systems can synchronize due to stable structures that emerge from chaotic activity. These structures are known as fractals, shapes with patterns which repeat over and over again in different scales of the shape. As chaotic systems are being coupled, the fractal structures of the different systems will start to assimilate with each other, taking the same form, causing the systems to synchronize. >>️

<< If the systems are strongly coupled, the fractal structures of the two systems will eventually become identical, causing complete synchronization between the systems. These findings help us understand how synchronization and self-organization can emerge from systems that didn't have these properties to begin with, like chaotic systems and biological systems. >>️

Topological synchronization of chaotic systems. Bar-Ilan University. Apr 22, 2022. 

https://phys.org/news/2022-04-topological-synchronization-chaotic.html

<< chaotic synchronization has a specific trait in various systems, from continuous systems and discrete maps to high dimensional systems: synchronization initiates from the sparse areas of the attractor, and it creates what (AA) termed as the ‘zipper effect’, a distinctive pattern in the multifractal structure of the system that reveals the microscopic buildup of the synchronization process. >>️

Lahav, N., Sendina-Nadal, I., et al. Topological synchronization of chaotic systems. Sci Rep 12, 2508. doi: 10.1038/ s41598-022-06262-z. Feb 15, 2022. 

https://www.nature.com/articles/s41598-022-06262-z

Also

keyword 'self-assembly' in FonT

https://flashontrack.blogspot.com/search?q=self-assembly

Keywords: gst, self-assembly, self-organization, fractals, topological synchronization, zipper effect, chaos, chaotic systems

# life: a proposito di vaticini ...

a proposito di vaticini (dal lat.  vates «vate» e canĕre «cantare» )...

Mr. Mario Draghi, la simmetria rifiutata ... 

Simmetrico, purtuttavia caotico. FonT. 19 luglio 2019.

https://flashontrack.blogspot.com/2019/07/life-simmetrico-purtuttavia-caotico.html

Anche

Be careful ... by Potus Joe. FonT. 11 maggio 2022. 

https://flashontrack.blogspot.com/2022/05/life-be-careful-by-potus-joe.html

Anche

Eight new echoing black hole binaries (in Milky Way). FonT. 25 giugno 2022. 

https://flashontrack.blogspot.com/2022/06/astro-eight-new-echoing-black-hole.html

Anche

non saprei dire il perchè ma le vicende governative di Mr Mario Draghi mi hanno fatto ricordare le 'bizzarre visioni' degli Artisti Aldo, Giovanni e Giacomo nell'episodio 'Il Conte Dracula' ... 

(1)   

https://youtu.be/gZNBR4YTSLs

(2)   

https://youtu.be/m9uRj9fV-i4

Keywords: symmetry, chaos, black hole, Mario Draghi, Gov

# gst: apropos of prolate- oblate spheroid transition, the chaotic behavior of a spinless entity around a black hole.

AA << investigate the long-term orbital dynamics of spinless extended bodies in Schwarzschild geometry, and show that periodic deviations from spherical symmetry in the shape of a test body may trigger the onset of chaos. (AA) do this by applying Dixon's formalism at quadrupolar order to a nearly spherical body whose shape oscillates between a prolate and an oblate spheroid. The late-time chaotic behavior is then verified by applying Melnikov's method. >>️

Ricardo A. Mosna, Fernanda F. Rodrigues, Ronaldo S. S. Vieira. Chaotic dynamics of a spinless axisymmetric extended body around a Schwarzschild black hole. arXiv: 2207.04341v1 [gr-qc]. Jul 9, 2022. 

https://arxiv.org/abs/2207.04341

Phys. Rev. D 106, 024016 (2022). 

https://doi.org/10.1103/PhysRevD.106.024016

Also - Oblate and Prolate Spheroid.  

<< The shape of the earth is that of a round ball or sphere slightly flattened at two opposite sides. Such a body is termed a spheroid. There are two kinds of spheroids-oblate and prolate; the former as the shape of an orange, the latter that of a lemon.  >>️

Oblate and Prolate Spheroid.  

https://etc.usf.edu/clipart/30500/30587/spheroid_30587.htm

img    https://etc.usf.edu/clipart/30500/30587/spheroid_30587_sm.gif

Also

keyword 'transition' in FonT: 

https://flashontrack.blogspot.com/search?q=transition

keyword 'transizione' | 'transition' in Notes (quasi-stochastic poetry): 

https://inkpi.blogspot.com/search?q=transizione

https://inkpi.blogspot.com/search?q=transition

Keywords: gst, spheroid, behavior, chaos, transition, black hole

# gst: non-trivial behaviors of a rotating (physical) double pendulum

<< The double pendulum, a simple system of classical mechanics, is widely studied as an example of, and testbed for, chaotic dynamics. In 2016, Maiti et al. studied a generalization of the simple double pendulum with equal point-masses at equal lengths, to a rotating double pendulum, fixed to a coordinate system uniformly rotating about the vertical. In this paper, (AA) study a considerable generalization of the double pendulum, constructed from physical pendula, and ask what equilibrium configurations exist for the system across a comparatively large parameter space, as well as what bifurcations occur in those equilibria. >>️

<< the non-trivial bifurcation (AA) have found (..), may actually be rightly understood as three additional bifurcations: there is a narrow region, approximately the ‘crease’ of the surface in Fig. 5, within which a vertical line (..) intersects the surface three times; (..). Thus three non-trival bifurcations would be expected in the corresponding bifurcations plots. >>️

Jonathan Tot, Robert H. Lewis. On the Equilibria and Bifurcations of a Rotating Double Pendulum. arXiv:2204.12437v2 [math.DS]. May 7, 2022. 

https://arxiv.org/abs/2204.12437

Also

keyword 'pendulum' in FonT

https://flashontrack.blogspot.com/search?q=pendulum

keyword 'pendolo' | 'pendola' in Notes

(quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=pendolo

https://inkpi.blogspot.com/search?q=pendola

Keywords: gst, pendulum, double pendulum, behavior, chaos 

# gst: even tight-binding billiards could exhibit chaotic behaviors

<< Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common property of all quantum-chaotic quadratic Hamiltonians studied in this context so far is the presence of random terms that act as a source of disorder. >>

AA << introduce tight-binding billiards in two dimensions, which are described by non-interacting spinless fermions on a disorder-free square lattice subject to curved open boundaries. >>

They <<  show that many properties of tight-binding billiards match those of quantum-chaotic quadratic Hamiltonians (..) these properties indeed appear to be consistent with the emergence of quantum chaos in tight-binding billiards. This statement nevertheless needs to be taken with some care since there exist a sub-extensive (in lattice volume) set of single-particle eigenstates that are degenerate in the middle of the spectrum at zero energy (i.e., zero modes), for which the agreement with RMT (random matrix theory) predictions may not be established. >>

Iris Ulcakar, Lev Vidmar. Tight-binding billiards. arXiv:2206.07078v1 [cond-mat.stat-mech]. Jun 14, 2022. 

https://arxiv.org/abs/2206.07078

Also

keyword 'billiard' in FonT

https://flashontrack.blogspot.com/search?q=billiard

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

keywords: gst, billiard, chaos, chaotic behavior

# gst: the solitary route to chimera states.

AA << show how solitary states in a system of globally coupled FitzHugh-Nagumo oscillators can lead to the emergence of chimera states. By a numerical bifurcation analysis of a suitable reduced system in the thermodynamic limit (they) demonstrate how solitary states, after emerging from the synchronous state, become chaotic in a period-doubling cascade. Subsequently, states with a single chaotic oscillator give rise to states with an increasing number of incoherent chaotic oscillators. In large systems, these chimera states show extensive chaos. (AA) demonstrate the coexistence of many of such chaotic attractors with different Lyapunov dimensions, due to different numbers of incoherent oscillators. >>

<<  While it is well known that self-organized wave patterns typically coexist within an interval of possible different wave numbers (..)(AA) show here the coexistence of coherence-incoherence patterns with different numbers of incoherent oscillators, which are in fact coexisting chaotic attractors with different Lyapunov dimensions. The incoherent oscillators in these coexisting attractors show extensive chaos of different dimensions. The total share of incoherent oscillators in a chimera state is a macroscopic quantity. Hence, within the range of such shares, where stable chimera states exist, (AA) find, for large systems, an increasing number of coexisting attractors with their numbers of incoherent oscillators increasing as well. (They) showed that, varying the coupling parameter, this extensive scenario is linked to the thermodynamic limit of the solitary regime, where the range of admissible numbers of incoherent oscillators shrinks down to one single oscillator in an infinitely large system. For this case, the emergence of the chaotic motion of the single incoherent oscillator could be shown in a period doubling cascade. >>

Leonhard Schulen, Alexander Gerdes, et al. The solitary route to chimera states. arXiv:2204.00385v1 [nlin.CD]. Apr 1, 2022.

https://arxiv.org/abs/2204.00385

Also

keyword 'FitzHugh-Nagumo oscillators' in APS | PubMed

https://journals.aps.org/search/

https://pubmed.ncbi.nlm.nih.gov/?term=FitzHugh-Nagumo+oscillators

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

keywords: gst, solitons, solitary states, period-doubling cascade, chaos, Lyapunov dimension, FitzHugh-Nagumo oscillator, chimera state, dynamical systems.

# gst: solitary wave billiards

<<  In the present work (AA) introduce the concept of solitary wave billiards. I.e., instead of a point particle, (they) consider a solitary wave in an enclosed region and explore its collision with the boundaries and the resulting trajectories in cases which for particle billiards are known to be integrable and for cases that are known to be chaotic. A principal conclusion is that solitary wave billiards are generically found to be chaotic even in cases where the classical particle billiards are integrable. However, the degree of resulting chaoticity depends on the particle speed and on the properties of the potential. >>

J. Cuevas-Maraver, P.G. Kevrekidis, H. Zhang. Solitary wave billiards. arXiv: 2203.09489v1 [nlin.PS]. Mar 17, 2022. 

https://arxiv.org/abs/2203.09489

Also 

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

keyword | 'soliton' in FonT

https://flashontrack.blogspot.com/search?q=soliton

keywords: gst, waves, solitons, billiard, chaos 

# gst: apropos of a immaginary transition (with a tipping point), which simulates the chaotic interactions of three black holes.

<< The interactions between three bodies such as stars or planets or black holes cannot be predicted with an elegant formula. Moerman (Arend Moerman) therefore used a computer that calculates what happens for a short period of time and then uses the result for the next period of time. >>

AA << varied the masses of the three interacting black holes. They started with one solar mass and went up to a billion times the mass of the sun. >>

<< Around ten million solar masses, there appeared to be a tipping point. In the simulations, black holes that are lighter than about ten million solar masses mostly eject each other through a gravitational slingshot. Black holes heavier than about ten million solar masses start to merge. First, two black holes merge. The third black hole will follow later. The black holes merge because they lose kinetic energy and that is because they emit gravitational waves. >>

<< Arend's work (..) has led to a new understanding of how black holes become supermassive. In the simulations, we see that heavy black holes no longer endlessly move around each other, but that, if they are heavy enough, they collide pretty much instantly. >> Simon Portegies Zwart. 

Simulating chaotic interactions of three black holes. Netherlands Research School for Astronomy. Oct 20, 2021. 

https://phys.org/news/2021-10-simulating-chaotic-interactions-black-holes.html

Tjarda C. N. Boekholt, Arend Moerman, Simon F. Portegies Zwart. Relativistic Pythagorean three-body problem. Phys. Rev. D 104, 083020. 14 Oct 14,  2021. 

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.104.083020

Also

more on the three-body problem (695 families of collisionless orbits). FonT. Oct 16, 2017. 

https://flashontrack.blogspot.com/2017/10/gst-more-on-three-body-problem-695.html

keyword 'black hole' | 'astro' in FonT

https://flashontrack.blogspot.com/search?q=black+hole

https://flashontrack.blogspot.com/search?q=astro

keyword 'transition' | 'transitional' in FonT

https://flashontrack.blogspot.com/search?q=transition

https://flashontrack.blogspot.com/search?q=transitional

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=transition

https://inkpi.blogspot.com/search?q=transizione

https://inkpi.blogspot.com/search?q=transizioni

keywords: gst, black hole, three-body problem, transition, chaos, chaotic interaction, tipping point.

# gst: Parrondo paradox revisited, a chaotic switching approach

<< Parrondo's paradox is a phenomenon where the switching of two losing games results in a winning outcome. >>

<< Suppose I present to you the outcome of the quantum walker at the end of 100 coin tosses, knowing the initial position, can you tell me the sequence of tosses that lead to this final outcome?" (..) In the case of random switching, it is almost impossible to determine the sequence of tosses that lead to the end result. However, for periodic tossing, we could get the sequence of tosses rather easily, because a periodic sequence has structure and is deterministic. >> Joel Lai.

<< This led to the idea of incorporating chaotic sequences as a means to perform the switching. The authors discovered that using chaotic switching through a pre-generated chaotic sequence significantly enhances the work. For an observer who does not know parts of the information required to generate the chaotic sequence, deciphering the sequence of tosses is analogous to determining a random sequence. However, for an agent with information on how to generate the chaotic sequence, this is analogous to a periodic sequence. According to the authors, this information on generating the chaotic sequence is likened to the keys in encryption. >>

Using quantum Parrondo's random walks for encryption. Singapore University of Technology and Design. Oct15, 2021.

https://phys.org/news/2021-10-quantum-parrondo-random-encryption.html

Joel Weijia Lai, Kang Hao Cheong. Chaotic switching for quantum coin Parrondo's games with application to encryption. Phys. Rev. Research 3, L022019. June 2, 2021. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.L022019

Also

<< usando l'output di una logistica (per certi valori dei parms) un ipotetico Donald potrebbe avere il vezzo di ottenere stessi risultati con serialita' numerica generata meccanicamente anziche' in modalita' casuale; >>️

#POTUS race: Donald, what he can do (with less than four lines ...). FonT. May 23, 2016. 

https://flashontrack.blogspot.com/2016/05/p-usa-potus-race-donald-what-he-can-do.html

Also

keyword 'parrondo' in FonT

https://flashontrack.blogspot.com/search?q=parrondo

keyword 'parrondo' in Notes  (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=parrondo

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keyword 'chaos' | 'chaotic' in Font

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keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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keywords: gst, games, life, chaos, Parrondo, Parrondo chaotic switching approach