# gst: apropos of interweavings, linking dispersion and stirring in randomly braiding flows.

     Fig. 5 (a)

<< Many random flows, including 2D unsteady and stagnation-free 3D steady flows, exhibit non-trivial braiding of pathlines as they evolve in time or space. (AA) show that these random flows belong to a pathline braiding 'universality class' that quantitatively links dispersion and chaotic stirring, meaning that the Lyapunov exponent can be estimated from the purely advective transverse dispersivity. (AA) verify this quantitative link for both unsteady 2D and steady 3D random flows. This result uncovers a deep connection between transport and mixing over a broad class of random flows. >>️

Daniel R. Lester, Michael G. Trefry, Guy Metcalfe. Linking Dispersion and Stirring in Randomly Braiding Flows. arXiv: 2412.05407v1 [physics.flu-dyn]. Dec 6, 2024.

https://arxiv.org/abs/2412.05407

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

Keywords: gst, random, random flows, randomly braiding flows, chaos

# gst: self-organized chimera states in pulse-coupled oscillator systems.

<< Coupled oscillator systems can lead to states in which synchrony and chaos coexist. These states are called “chimera states.” >>

️

AA << study a variation of a pulse-coupled oscillator (PCO) model that has been shown to produce chimera states, demonstrate that it reproduces several of the expected chimera properties, like the formation of multiple heads and the ability to control the natural drift that Kuramoto's chimera states experience in a ring, and explain how chimera states emerge. >>️

<< Three notable aspects of chimeras in our PCO networks (with time-discrete coupling) are the absence of firing events from the tail (which still almost synchronize their phases), the reliable onset of the phenomenon from virtually any initial configuration, and the lack of a superimposed structure (e.g., artificially splitting the population into subgroups) and thus the self-organized nature of the phenomenon. >>️

Arke Vogell, Udo Schilcher, et al. Chimera states in pulse-coupled oscillator systems. Phys. Rev. E 110, 054214. Nov 26, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.054214 

Also: chimera, self-assembly, chaos, network,  in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, self-assembly, chaos, network 

# game: balance exploration and exploitation, making decisions cooperatively without sharing information.

<< Multiagent reinforcement learning (MARL) studies crucial principles that are applicable to a variety of fields, including wireless networking and autonomous driving. (AA) propose a photonic-based decision-making algorithm to address one of the most fundamental problems in MARL, called the competitive multiarmed bandit (CMAB) problem. >>

AA << demonstrate that chaotic oscillations and cluster synchronization of optically coupled lasers, along with (their) proposed decentralized coupling adjustment, efficiently balance exploration and exploitation while facilitating cooperative decision making without explicitly sharing information among agents. >>

AA << study demonstrates how decentralized reinforcement learning can be achieved by exploiting complex physical processes controlled by simple algorithms. >>

Shun Kotoku, Takatomo Mihana, et al. Decentralized multiagent reinforcement learning algorithm using a cluster-synchronized laser network. Phys. Rev. E 110, 064212. Dec 11, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.064212

Img: https://x.com/PhysRevE/status/1866889144657465632

Also: game, chaos, ai (artificial intell), in https://www.inkgmr.net/kwrds.html 

Keywords: game, cooperation, chaos, exploration, exploitation, ai, artificial intelligence, MARL, CMAB.

# gst: protected chaos in a topological lattice.

<< The erratic nature of chaotic behavior is thought to erode the stability of periodic behavior, including topological oscillations. However, (AA) discover that in the presence of chaos, non-trivial topology not only endures but also provides robust protection to chaotic dynamics within a topological lattice hosting non-linear oscillators. >>

<< Despite the difficulty in defining topological invariants in non-linear settings, non-trivial topological robustness still persists in the parametric state of chaotic boundary oscillations. (AA) demonstrate this interplay between chaos and topology by incorporating chaotic Chua's circuits into a topological Su-Schrieffer-Heeger (SSH) circuit. >>

<< By extrapolating from the linear limit to deep into the non-linear regime, (AA) find that distinctive correlations in the bulk and edge scroll dynamics effectively capture the topological origin of the protected chaos. (Their)  findings suggest that topologically protected chaos can be robustly achieved across a broad spectrum of periodically-driven systems, thereby offering new avenues for the design of resilient and adaptable non-linear networks. >>️

Haydar Sahin, Hakan Akgün, et al. Protected chaos in a topological lattice. arXiv: 2411.07522v1 [cond-mat.mes-hall]. Nov 12, 2024.

https://arxiv.org/abs/2411.07522

Also: chaos, random, instability, transition, network, ai (artificial intell), in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, random,  instability, transition, network, AI, Artificial Intelligence

# gst: apropos of transverse instabilities, from chimeras to extensive chaos

<< Populations of coupled oscillators can exhibit a wide range of complex dynamical behavior, from complete synchronization to chimera and chaotic states. We can thus expect complex dynamics to arise in networks of such populations. >>️

Here AA << analyze the dynamics of networks of populations of heterogeneous mean-field coupled Kuramoto-Sakaguchi oscillators, and show that the instability that leads to chimera states in a simple two-population model also leads to extensive chaos in large networks of coupled populations. >>️

Pol Floriach, Jordi Garcia-Ojalvo, Pau Clusella. From chimeras to extensive chaos in networks of heterogeneous Kuramoto oscillator populations. arXiv: 2407.20408v2 [nlin.CD]. Oct 11, 2024.

https://arxiv.org/abs/2407.20408

Also: chimera, instability, chaos, network, in 

https://www.inkgmr.net/kwrds.html 

Keywords: gst, chimera, instability, chaos, network

# gst: isles of regularity (depending on the initial setup) in a sea of chaos amid the gravitational three-body problem.

AA << study probes the presence of regular (i.e. non-chaotic) trajectories within the 3BP (three-body problem) and assesses their impact on statistical escape theories. >>

AA << analysis reveals that regular trajectories occupy a significant fraction of the phase space, ranging from 28% to 84% depending on the initial setup, and their outcomes defy the predictions of statistical escape theories. The coexistence of regular and chaotic regions at all scales is characterized by a multi-fractal behaviour. >>

Alessandro Alberto Trani, Nathan W.C. Leigh, et al. Isles of regularity in a sea of chaos amid the gravitational three-body problem. A&A, 689, A24, Jun 25, 2024.

https://www.aanda.org/articles/aa/full_html/2024/09/aa49862-24/aa49862-24.html

"Islands" of Regularity Discovered in the Famously Chaotic Three-Body Problem. University of Copenhagen. Oct 11, 2024.

https://science.ku.dk/english/press/news/2024/islands-of-regularity-discovered-in-the-famously-chaotic-three-body-problem/

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

Keywords: gst, three balls, escape, chaos, transition 

# gst: dynamics of pulsating spheres orbiting black holes.

AA << study the chaotic dynamics of spinless extended bodies in a wide class of spherically symmetric spacetimes, which encompasses black-hole scenarios in many modified theories of gravity. (They) show that a spherically symmetric pulsating ball may have chaotic motion in this class of spacetimes. >>

AA << use Melnikov's method to show the presence of homoclinic intersections, which imply chaotic behavior, as a consequence of (their)  assumption that the test body has an oscillating radius. >>

Fernanda de F. Rodrigues, Ricardo A. Mosna, Ronaldo S. S. Vieira. Chaotic dynamics of pulsating spheres orbiting black holes. arXiv: 2409.14667v1 [gr-qc]. Sep 23, 2024.

https://arxiv.org/abs/2409.14667

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

Keywords: gst, black hole, homoclinic orbit, chaos, transition

# gst: apropos of intermittent switchings, presence of chaotic saddles in fluid turbulence.

<< Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid turbulence. They differ from the intermittency of a low-dimensional system accompanied by the stability change of a fixed point or a periodic orbit in that the intermittency of a high-dimensional system tends to appear in a wide range of parameters. >>️

Here AA << demonstrate the presence of chaotic saddles underlying intermittency in fluid turbulence and phase synchronization. Furthermore, (they) confirm that chaotic saddles persist for a wide range of parameters. Also, a kind of phase synchronization turns out to occur in the turbulent model. >>️

Hibiki Kato, Miki U Kobayashi, et al. A laminar chaotic saddle within a turbulent attractor. arXiv: 2409.08870v1 [nlin.CD]. Sep 13, 2024. 

https://arxiv.org/abs/2409.08870

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

Keywords: gst, transition, turbulence, intermittency, chaos

# gst: a body of revolution with a cat’s toy mechanism.

AA << introduce a class of examples which provide an affine generalization of the nonholonomic problem of a convex body rolling without slipping on the plane. >>

️

They << prove that (this system can be) integrable if the generalized momentum M is vertical (i.e. parallel to γ) and exhibit numerical evidence that it is chaotic otherwise. >>️

M. Costa Villegas, L.C. García-Naranjo. Affine generalizations of the nonholonomic problem of a convex body rolling without slipping on the plane. arXiv: 2409.08072v1 [math-ph]. Sep 12, 2024. 

https://arxiv.org/abs/2409.08072

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

Keywords: gst, transition, chaos

# gst: networks of pendula with diffusive interactions, chaotic regime seems to emerge at low energies.

AA << study a system of coupled pendula with diffusive interactions, which could depend both on positions and on momenta. The coupling structure is defined by an undirected network, while the dynamic equations are derived from a Hamiltonian; as such, the energy is conserved. >>️

<< The behaviour observed showcases a mechanism for the appearance of chaotic oscillations in conservative systems. For Hamiltonians with two degrees of freedom, it has been shown how chaos can emerge near a saddle-centre equilibrium possessing a homoclinic orbit. (AA) have seen that higher-dimensional systems having mixed equilibria, i.e., generalisations of a saddle-center where the eigenvalues are only imaginary and reals, also show chaotic behaviour close to those points.  >>️

AA << complement the analysis with some numerical simulations showing the interplay between bifurcations of the origin and transitions to chaos of nearby orbits. A key feature is that the observed chaotic regime emerges at low energies. >>

️

Riccardo Bonetto, Hildeberto Jardón-Kojakhmetov, Christian Kuehn. Networks of Pendula with Diffusive Interactions. arXiv: 2408.02352v1 [math.DS]. Aug 5, 2024.

https://arxiv.org/abs/2408.02352

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

Keywords: gst, pendulum, network, transition, chaos, bifurcation

# game: hypothesis of a geometric design of chaotic attractors, on demand

AA << propose a method using reservoir computing to generate chaos with a desired shape by providing a periodic orbit as a template, called a skeleton. (They) exploit a bifurcation of the reservoir to intentionally induce unsuccessful training of the skeleton, revealing inherent chaos. The emergence of this untrained attractor, resulting from the interaction between the skeleton and the reservoir's intrinsic dynamics, offers a novel semi-supervised framework for designing chaos. >>️

Tempei Kabayama, Yasuo Kuniyoshi, et al. Designing Chaotic Attractors: A Semi-supervised Approach. arXiv: 2407.09545v1 [cs.NE]. Jun 27, 2024.

https://arxiv.org/abs/2407.09545

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

Keywords: game, chaos, chaotic attractors

# gst: Resonancelike emergence of chaos in complex networks of damped-driven nonlinear systems.

AA << solve a critical outstanding problem in this multidisciplinary research field: the emergence and persistence of spatiotemporal chaos in complex networks of damped-driven nonlinear oscillators in the significant weak-coupling regime, while they exhibit regular behavior when uncoupled. >>

They << uncover and characterize the basic physical mechanisms concerning both heterogeneity-induced and impulse-induced emergence, enhancement, and suppression of chaos in starlike and scale-free networks of periodically driven, dissipative nonlinear oscillators. >>️

Ricardo Chacon, Pedro J. Martínez. Resonancelike emergence of chaos in complex networks of damped-driven nonlinear systems. Phys. Rev. E 110, 014209. Jul 19, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.014209

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

Keywords: gst, network, resonance, chaos

# gst: apropos of the transition of order from chaos, a universal behavior near a critical point.

<< As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, (AA) observe the emergence of a single dominant timescale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. >>️

AA << study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system.   >>️

<< the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. (AA) results show that the observed emergence of order from chaos is a continuous phase transition (..) the critical exponents characterizing this transition fall in the universality class of directed percolation. >>️

The << paper demonstrates how a real-world complex, nonequilibrium turbulent reactive flow system exhibits universal behavior near a critical point. >>️

Sivakumar Sudarsanan, Amitesh Roy, et al. Emergence of order from chaos through a continuous phase transition in a turbulent reactive flow system. Phys. Rev. E 109, 064214. Jun 20, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.064214

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

Keywords: gst, order, chaos, transition 

# 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: 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: chaos creates and destroys branched flows.

<< Electrons, lasers, tsunamis, and ants have at least one thing in common: they all display branched flow. Whenever a wave propagates through a weakly refracting medium, flow is expected to accumulate along certain directions, forming structures called branches. >>️

AA << explore the laws governing the evolution of the branches in periodic potentials. On one hand, (They) observe that branch formation follows a similar pattern in all non-integrable potentials, no matter whether the potentials are periodic or completely irregular. Chaotic dynamics ultimately drives the birth of the branches. On the other hand, (AA) results reveal that for periodic potentials the decay of the branches exhibits new characteristics due to the presence of infinitely stable branches known as superwires.  >>️

Alexandre Wagemakers, Aleksi Hartikainen, et al. Chaotic dynamics creates and destroys branched flow. arXiv: 2406.12922v1 [nlin.PS]. Jun 14, 2024. 

https://arxiv.org/abs/2406.12922

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

Keywords: gst, chaos, transition, branched flows, superwires 

# gst: elasticity of fibres prefers the chaos of turbulence.

FIG. 4. Maximal Lyapunov exponents λ1 associated with the flow regions sampled by the fibre centre of masses in a 3D turbulent flow. 

<< Turbulent flows are ubiquitous in nature and are responsible for numerous transport phenomena that help sustain life on earth. >>️

AA << have shown that the stretching of fibres is due only to elasticity and their inertia playing a minimal role as they are advected by a turbulent carrier flow. A highly elastic fibre is much more likely to be stretched out and as a result prefers a “straighter” configuration rather than a coiled one. >>️

<< These inertial, elastic fibres then exhibit non-trivial preferential sampling of a 3D turbulent flow in a manner qualitatively similar to 2D turbulence (..). Inertia leads fibres away from vortical regions while their elasticity pulls them inside the vortices. Upto a moderate inertia (St ∼ O(1)), fibres increasingly prefer the straining regions of the flow, while at much larger inertia (St ≫ 1) they decorrelate from the flow and preference for straining regions begins to diminish again. >>️

<< However, owing to a large elasticity, fibres get trapped in vortical regions (at small St), as well as are unable able to exit the straining regions quickly. A more elastic and extensible fibre is, thus, more likely to spend longer times in both vortical and the straining regions of the flow. >>️

<< This picture of preferential sampling of a 3D turbulent flow by elastic, inertial fibres is also confirmed by alternately studying the chaoticity of the sampled flow regions via Lyapunov Exponents. Less elastic fibres prefer less chaotic (vortical) regions of the flow while more chaotic (straining) regions are preferred at large Wi. LEs also confirm that preferential sampling has a non-monotonic dependence on St for small elasticity but which is lost when Wi becomes very large.  >>

<< It would (..) be even more interesting to see how chaotic the fibre trajectories themselves are and what that has to say about fibre dynamics in turbulent flows. >>️

️

Rahul K. Singh. Elasticity of fibres prefers the chaos of turbulence. arXiv: 2406.06033v1. Jun 10, 2024.

https://doi.org/10.48550/arXiv.2406.06033

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

Keywords: gst, elastic, chaos, turbulence

# gst: chaos controlled and disorder driven phase transitions by breaking permutation symmetry

<< Introducing disorder in a system typically breaks symmetries and can introduce dramatic changes in its properties such as localization. At the same time, the clean system can have distinct many-body features depending on how chaotic it is. >>

<< In this work the effect of permutation symmetry breaking by disorder is studied in a system which has a controllable and deterministic regular to chaotic transition. >>

<< Results indicate a continuous phase transition from an area-law to a volume-law entangled phase irrespective of whether there is chaos or not, as the strength of the disorder is increased. The critical disorder strength obtained by finite size scaling, indicate a strong dependence on whether the clean system is regular or chaotic to begin with. >>

<< Additionally, (AA) find that a relatively small disorder is seen to be sufficient to delocalize a chaotic system. >>

Manju C, Arul Lakshminarayan, Uma Divakaran. Chaos controlled and disorder driven phase transitions by breaking permutation symmetry. arXiv: 2406.00521v1 [quant-ph]. Jun 1, 2024. 

https://arxiv.org/abs/2406.00521

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

Keywords: gst, transition, chaos, disorder 

FonT: who is Manju C?

# gst: periodic defect braiding in active nematics confined to a cardioid.

AA' paper << examines self-mixing in active nematics, a class of fluids in which mobile topological defects drive chaotic flows in a system comprised of biological filaments and molecular motors. (They) present experiments that demonstrate how geometrical confinement can influence the braiding dynamics of the defects. >>️

<< Notably, (AA) show that confinement in cardioid-shaped wells leads to realization of the golden braid, a maximally efficient mixing state of exactly three defects with no defect creation or annihilation. >>

<< Increasing the size of the confining cardioid produces a transition from the golden braid, to the fully chaotic active turbulent state. >>️️

Fereshteh L. Memarian, Derek Hammar, et al. Controlling Chaos: Periodic Defect Braiding in Active Nematics Confined to a Cardioid. Phys. Rev. Lett. 132, 228301. May 28, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.228301

https://x.com/PhysRevLett/status/1796622457303876000

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

Keywords: gst, chaos, turbulence, active nematics, cardioid

# gst: relativistic chaotic scattering, scaling laws for trapped trajectories.

AA << study different types of phase space structures which appear in the context of relativistic chaotic scattering. By using the relativistic version of the Hénon-Heiles Hamiltonian, (They) numerically study the topology of different kind of exit basins and compare it with the case of low velocities in which the Newtonian version of the system is valid. >>

<< In all cases, fractal structures are present, and the escaping dynamics is characterized. In every case a scaling law is numerically obtained in which the percentage of the trapped trajectories as a function of the relativistic parameter β and the energy is obtained. >>

Their << work could be useful in the context of charged particles which eventually can be trapped in the magnetosphere, where the analysis of these structures can be relevant. >>️

Fernando Blesa, Juan D. Bernal, et al. Relativistic chaotic scattering: Unveiling scaling laws for trapped trajectories. Phys. Rev. E 109, 044204. Apr 5, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.044204

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

Keywords: gst, chaos, chaotic, escape, escape trajectories