# gst: using analogues to investigate error growth and predictability in turbulence.

<< ️In this study, (AA) revisit Lorenz's pioneering concept of analogues to investigate error growth and predictability in fully developed turbulence using experimental data. By applying the method to a 1D turbulent velocity time series, (They) successfully identify the three error growth regimes intuited by Lorenz and later formalized by turbulence theory: the chaotic exponential regime, the algebraic regime of spontaneous stochasticity, and the saturation regime. >>

<< (AA) analysis reveals that the Lyapunov exponent and the exponent of the algebraic regime depend on the initial error. (They) interpret this dependence as a statistical bias induced by the intermittency of turbulence, where rare events, characterized by lower Lyapunov exponents and more singular velocity increments, are preferentially sampled when considering larger initial errors. >>

<< ️These findings not only validate Lorenz's qualitative intuition but also provide new quantitative insights into the predictability of turbulent flows, paving the way for potential applications in the prediction of extreme events. >>

Carlos Granero-Belinchon, Mickaël Bourgoin, Bérengère Dubrulle. Using analogues to investigate error growth and predictability in turbulence. arXiv: 2610.11796v1 [physics.flu-dyn]. Oct 8, 2026.

https://arxiv.org/abs/2610.11796

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

Keywords: gst, chaos, turbulence, error, analogy, intermittency, rare events, Lorenz's error growth regimes, chaotic exponential regime, algebraic regime of spontaneous stochasticity, saturation regime, transitions.

# gst: extreme events in an active fluid medium.

<< ️(AA) observe the emergence of extreme events in an active fluid involving two distinct chemical species that regulate active stress. One species is slow diffusing and the other is fast diffusing, and the growth of the fast-diffusing species is modelled using a nonlinear logistic term. >>

<< ️(AA) demonstrate the presence of extreme events in the temporal evolution of the concentrations, as well as in the spatial profile of the system,in regimes of merging-emerging soliton-like dynamics and spatio-temporal chaos, through analysis of the time-series, bifurcation diagrams, probability distribution functions of the concentration of the two species, return maps and distributions of inter-event intervals. >>

<< ️Interestingly, (They) also find evidence of pronounced bunching of extreme events and super-extreme events in the slow chemical species in the soliton-like regime. (They) go on to systematically explore the dependence of the extreme event occurrences on the Péclet number and the strength of the nonlinear growth term, and find that the probability of extreme events increases after a critical Péclet number, while increasing the nonlinearity suppresses extreme events. >>

<< ️Lastly, in order to gain further insight, (AA) investigate a modified mode-truncated reduced order model comprising of coupled differential equations mimicking this active fluid system. (They) find that this reduced order model also exhibits extreme events whose emergence is correlated with a sudden expansion in attractor size due to a crisis arising from attractor collision. >>

<< ️So these results demonstrate the existence of extreme events in an active fluid system, and are of potential relevance to biological phenomena where active transport plays an important role. >>

Joydeep Das, Abhishek Chaudhuri, Sudeshna Sinha. Extreme Events in an Active Fluid Medium. arXiv: 2609.14334v1 [nlin.PS]. Sep 13, 2026.

https://arxiv.org/abs/2609.14334

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

Keywords: gst, chaos, solitons, attractors, extreme events, merging-emerging soliton-like dynamics, soliton-like regimes, criticality, active transport.

# gst: shear v. stretching as drivers for mixing in 3-D porous media flows.

<< ️Solute mixing in porous media results from the interplay between molecular diffusion and the deformation of fluid parcels, which elongates solute elements and steepens concentration gradients in the pore space. >> 

<< ️In three-dimensional porous media, fluid deformation is asymptotically governed by exponential stretching, arising from the chaotic stretching and folding of fluid elements. However, early-time deformation may be dominated by shear, induced by no-slip boundary conditions at grain surfaces, leading to linear elongation. Yet, the persistence and relative contributions of linear shear and exponential stretching to fluid deformation and solute mixing remain poorly understood. >>

<< ️Here, (AA) address this question using numerical simulations of fluid deformation and mixing in body-centered cubic bead packs, where the rate of chaotic stretching can be varied with the direction of flow, while maintaining the same average shear rate. (They) quantify the mean deformation dynamics of elementary surfaces as a function of their initial orientation with respect to streamlines, and their consequences on mixing through Lagrangian methods. >>

<< ️(AA) show that surface elements with certain initial orientations relative to the streamline direction experience a transient phase of shear-dominated deformation at early times, leading to persistently larger deformation compared to those with initial orientations that yield purely exponential growth. By expressing the deformation components in streamline coordinates, (They) derive approximate analytical expressions linking the different components of fluid deformation to shear, helicity, and chaotic stretching. (They) discuss consequences for the mixing of solute sheets and blobs, highlighting generic behaviors as well as differences between these two representations. >>

Manuel Maeritz, Tanguy Le Borgne, Daniel R. Lester, et al. Shear versus stretching as drivers for mixing in three-dimensional porous media flows. Phys. Rev. Fluids 11, 094501. Sep 17, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/4wyw-nkrb

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

Keywords: gst, chaotic advection, fluid deformation, flows in porous media, laminar flows, mixing enhancement, shear flows, chaotic stretching, porous media.

# gst: densely packed particle raft at vertically vibrated air-water interface.

<< ️(AA) investigate the dynamics of a dense raft of millimeter-sized granular particles at a vertically vibrated air-water interface, which displays a rich set of patterns and particle dynamics as we vary the vibration amplitude, frequency, and particle packing fraction. >>

<< ️While the classical parametric instability with standing waves still occurs over a certain range of parameters, the measured wave dispersion relations indicate an increasing role of the raft's emergent elasticity at higher packing fractions, where the effective surface tension decreases and the out-of-plane bending modulus increases. >>

<< ️At higher vibration frequencies and lower amplitudes, (They) identify a regime without standing waves. Instead, individual particles exhibit thermal-like motion, with transport crossing over from diffusive to sub-diffusive as the packing fraction increases. >>

<< ️The particle dynamics also display spatial and temporal heterogeneity, as in supercooled liquids. Starting from this regime, when the vibration amplitude is further increased, a large cavity eventually forms inside the raft, whose size and shape depend on the vibration frequency and the injected vibration energy. The cavitation results in the coexistence of free-surface water waves inside the cavity and thermal-like particle motion in the surrounding raft. >>

Xiuhe Yan, Tabitha C. Watson, Hongyi Xiao. Densely packed particle raft at vertically vibrated air-water interface. Phys. Rev. E 114, 025427. Aug 31, 2026.

https://journals.aps.org/pre/abstract/10.1103/95rf-w6fd

arXiv: 2602.17539v2 [cond-mat.soft]. 

https://arxiv.org/abs/2602.17539

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

Keywords: gst, particles, waves, instability,  transitions, elasticity, chaos, granular particles, air-water interface, raft elasticity, emergence of patterns, surface & interfacial phenomena, granular materials.

# gst: the ultimate state of elastic turbulence.

<< The asymptotic properties, with vanishing viscosity, of inertial turbulence in Newtonian fluids have been of intense scrutiny over the years. Much less is known about elastic turbulence - a distinct spatio-temporally chaotic state exhibited by viscoelastic fluids. >>

<< In this work, using direct numerical simulations of turbulence in a triperiodic box, (AA) show that elastic turbulence achieves an ultimate state with increasing polymer relaxation time, i.e., the Deborah number, for two different constitutive models (Oldroyd-B and FENE-P). >>

<< In the limiting state, various bulk quantities - the fluid dissipation, the polymeric energy transfer, as well as the elastic stresses - are shown to become independent of the polymer relaxation time scale, notwithstanding the microstructure deformation scales distinctly depending on the model. >>

Piyush Garg, Marco Edoardo Rosti. The ultimate state of elastic turbulence. arXiv: 2608.26479v1 [physics.flu-dyn]. Aug 27, 2026.

https://arxiv.org/abs/2608.26479

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

Keywords: gst, elasticity, turbulence, chaos, vanishing viscosity, inertial turbulence, elastic turbulence, elastic stress, viscoelastic fluids, polymer relaxation.

# gst: self-organizing chimera states in adaptive networks.

<< ️(AA) propose a minimal adaptive network model with product-form coupling that reduces dimensionality while capturing key features of synaptic plasticity. The system spontaneously self-organizes into adaptive chimera states, where identical oscillators separate into synchronized and desynchronized groups through adaptive weight dynamics. >>

<< These adaptive chimeras organize into branches with fixed coherent cluster fraction and exhibit transitions between stationary, breathing, and chaotic collective dynamics, revealing a collective bifurcation structure. Crucially, the resulting attractor landscape is highly multistable: repeated cluster reorganizations generate distinct dynamical pathways that coexist within the same parameter regime and depend sensitively on initial conditions. >>

Felix Augustsson, Rok Cestnik, Matthias Wolfrum, et al. Self-organizing Chimera States in Adaptive Networks. arXiv: 2608.20517v1 [nlin.AO]. Aug 20, 2026.

https://arxiv.org/abs/2608.20517

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

Keywords: gst, chimera, self-assembly, networks, transitions, brain, oscillators, adaptive chimera, synaptic plasticity, synchronized- desynchronized stationary states, breathing, chaotic collective dynamics, collective bifurcations, multistable attractors.

# gst: non-normal route to chaos

<< Deterministic chaos is usually associated with local spectral expansion: Jacobian eigenvalues are expected to exceed unity somewhere on the attractor. (AA) show that this view is incomplete in dimensions 𝑑>1. For non-normal Jacobians, pointwise spectral stability can suggest everywhere local contraction, while nonorthogonal eigenvectors still allow transient singular-vector amplification. >>

<< (AA) construct four low-dimensional deterministic maps realizing this mechanism: partition-reinjected, phase-prescribed, feedback-driven, and affine-reinjected non-normal routes to chaos. In all cases, the sampled one-step Jacobian remains spectrally stable at every point on the attractor away from switching boundaries, with the eigenvalues of the common planar core fixed inside the unit disk. Nevertheless, increasing non-normality raises the maximal Lyapunov exponent from negative to positive values, corresponding to sustained asymptotic chaos, not transient chaos. Across the four classes, the common signature is spectral radius 𝜌max traj<1, singular value 𝜎max traj>1, maximal Lyapunov exponent 𝜆1>0, and an increase of attractor dimension. >>

<< These examples identify non-normality and recurrent reinjection of transiently amplified directions as a deterministic route to chaos distinct from eigenvalue instability. >>

D. Sornette, V.R. Saiprasad, V. Troude. Non-normal route to chaos. Phys. Rev. E 114, 024222. Aug 27, 2026.

https://journals.aps.org/pre/abstract/10.1103/z9qv-51yj

arXiv: 2603.08191v2 [nlin.CD]. 

https://arxiv.org/abs/2603.08191

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

Keywords: gst, attractor, chaos, transitions

# gst: flip rate prediction in the double pendulum.

<< ️The intermediate-energy double pendulum is a prototypical chaotic system. Despite its irregular motion, it exhibits recurrent flips - events in which one of the arms passes over the top. >>

<< ️(AA) develop a statistical prediction for the mean flip rate in terms of phase space flux. Applying this flux-based approach to the equal-mass, equal arm ("egalitarian") double pendulum, (They) find excellent agreement between the statistical prediction and numerical simulations: ensemble-averaged flip rates agree at about the 1% level, while even the statistics of individual chaotic trajectories agree at the few-percent level, quantifying the validity of the ergodic approximation. This agreement holds for flips of either arm and over a broad range of energies. This flux-based approach is closely related to that used for the egalitarian three-body system. >>

<< ️A central role is played by the saddle orbits: periodic orbits that tend to the stable saddle eigenmode as the energy approaches the saddle energy from above and approximately follow the ridge of the potential at higher energies. These orbits provide a natural dividing surface for defining flips while avoiding recrossings. Indeed, the resulting distribution of crossing times exhibits a distinct gap. >>

<< ️(AA) also present two alternative simplified dividing surfaces, one of which is based on an accurate analytic approximation to the saddle orbits. >>

Peleg Haham, Barak Kol. Flip rate prediction in the double pendulum. arXiv: 2608.20276v1 [nlin.CD]. Aug 20, 2026.

https://arxiv.org/abs/2608.20276

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

Keywords: gst, pendulum, double pendulum, chaos, recurrent flips, egalitarian three-body system, saddle orbits, crossing times.

# gst: survival probability of particles inside the lemon billiard.

<< ️(AA) study the escape of particles in the lemon billiard, a two-parameter family of billiard systems defined by the intersection of two identical circles. Using numerical simulations, (They) explore how the survival probability depends on the position and size of the hole, as well as on the billiard shape parameter. >>

<< ️(AA) find that the survival probability exhibits a two-stage decay pattern: an initial exponential regime followed by a long-time power-law tail, a signature of the stickiness effect. (Their) results show that the short-time exponential decay rate follows a power-law dependence on the hole size, with different scaling exponents for holes placed in chaotic regions versus mixed phase-space regions. For holes located in mixed phase-space regions, the decay exponent of the long-time power-law tail remains approximately constant, while the amplitude follows a power-law scaling with hole size. >>

<< ️(They) also examine the dependence of short-time exponential decay rate on the billiard shape parameter and observe scaling behavior for small values of this parameter, which breaks down as the parameter increases. >>

Daniel Borin, Edson Denis Leonel, Diego Fregolent Mendes de Oliveira. Survival probability of particles inside the lemon billiard. Phys. Rev. E 114, 014224. Jul 28, 2026.

https://journals.aps.org/pre/abstract/10.1103/md5j-ggyd

arXiv: 2601.13000v1 [nlin.CD]. Jan 19, 2026.

https://arxiv.org/abs/2601.13000

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

Keywords: gst, billiard, particles, chaos, transitions, survival probability, two-stage decay pattern, stickiness effect, scaling behavior, scaling laws of complex systems. 

# gst: natural invariant measures for chaotic game dynamics; finding order in chaos.

<< ️(AA) study the long-term behavior of the Multiplicative Weights Update (MWU) algorithm in game settings where learning dynamics frequently fail to converge to Nash equilibria and instead exhibit Li-Yorke chaos. While such chaos precludes the prediction of specific long-term strategy profiles, it does not imply a lack of statistical structure. >>

<< ️(AA) demonstrate that natural invariant measures — a fundamental concept from ergodic theory — provide the rigorous framework necessary to find order within this chaos. Focusing on a two-strategy congestion game, (They) prove that these measures allow for a comprehensive statistical characterization of the dynamics. Crucially, (They) show that this framework extends beyond simple strategy frequencies to general observables, enabling the precise calculation of long-term time averages for broad classes of economic metrics — including payoffs, social cost, and regret — despite chaos. >>

<< ️(They) results reveal that this simple learning algorithm captures the full spectrum of behaviors found in one-dimensional dynamical systems, from unique or multiple absolutely continuous invariant measures to complex periodic attractors as well as coexisting chaotic and stable (periodic) behaviors. By bridging game theory and dynamical systems, (AA) show that statistical predictability is attainable even in the absence of pointwise convergence. >>

<< ️The intersection of game theory, dynamical systems, computer science, and statistics is rich with open questions, particularly when considering learning dynamics in games. >>

Jakub Bielawski, Thiparat Chotibut, Fryderyk Falniowski, et al. Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos. arXiv: 2607.21805v1 [math.DS]. Jul 23, 2026.

https://arxiv.org/abs/2607.21805

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

Keywords: gst, game, chaos, Multiplicative Weights Update (MWU) algorithm, statistical structure, statistical predictability, two-strategy congestion game, complex periodic attractors, coexisting chaotic and stable (periodic) behaviors.

# gst: emergence of minimal chimera in uncoupled oscillators under common frequency-modulated driving.

<< (AA) report the experimental realization of minimal chimera states in a system of three uncoupled oscillators driven solely by frequency-modulated forcing. Unlike conventional scenarios where chimera states emerge due to interactions among oscillators, here the coexistence of coherent and incoherent dynamics arises entirely from a common external modulation of a system parameter. By tuning the modulation amplitude and frequency, the system exhibits transitions between global synchronization, global incoherence, and minimal chimera states. >>

<< The stability of these regimes is quantified using the maximal Lyapunov exponent, while a synchronization order parameter is employed to characterize the degree of coherence. A systematic exploration of the parameter space reveals well-defined regions associated with distinct dynamical behaviors. To provide analytical understanding, (AA) employ a phase-reduction approach and derive the corresponding phase dynamics, which elucidate the mechanisms underlying phase locking and desynchronization. The robustness of the proposed mechanism is further demonstrated in a time-delayed chaotic system. >>

<< Finally, experimental results obtained from an electronic circuit realization confirm the emergence of minimal chimera states under frequency-modulated driving. These findings establish external modulation as a viable route to chimera formation without coupling, offering a new perspective on collective dynamics in driven nonlinear systems. >>

Debabrata Biswas, Tanmoy Banerjee. Emergence of minimal chimera in uncoupled oscillators under common frequency-modulated driving: theory and experiment. arXiv: 2607.25449v1 [nlin.CD]. Jul 28, 2026.

https://arxiv.org/abs/2607.25449

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

Keywords: gst, chimera, transition, chaos, three uncoupled oscillators, coherent- incoherent dynamics, frequency-modulated forcing, global synchronization, global incoherence, minimal chimera states.

# gst: dynamical origin of extreme events in mutually coupled and networked Brusselator.

<< This (AA) study investigates the dynamical origins and statistical properties of extreme events (EEs) in a diffusively coupled theoretical Brusselator system, extending from pairwise interactions to globally coupled networks. >>

<< Statistically, the emergence of EEs is characterized by heavy-tailed probability density functions and exponential interevent interval distributions, alongside an analysis of the complementary cumulative distribution function and return periods. To elucidate the underlying generative mechanism, (They) employ invariant manifold computations and vector field divergence analysis. >>

<< (Their) results demonstrate that EEs are triggered by a critical region formed by the geometric alignment of stable and unstable manifolds near a saddle-type invariant set governed by the Shilnikov mechanism. Furthermore, extending the analysis to a globally coupled network reveals that network dimensionality does not affect the prevalence of EEs. >>

<< Finally, these numerical findings are corroborated by experimental observations from an analog electronic circuit, confirming the robustness of these dynamical phenomena in physical systems. >>

S.V. Manivelan, S.Sabarathinam, K.Thamilmaran, et al. Dynamical origin of extreme events in mutually coupled and networked Brusselator. Phys. Rev. E 114, 014217. Jul 15, 2026.

https://journals.aps.org/pre/abstract/10.1103/byp5-gxrz  

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

Keywords: gst, networks, chaos, Brusselator, coupled oscillators, extreme event statistics, criticality, saddle-type invariant set.

# life: apropos of bifurcations from stable consensus to periodic multiconsensus, consensus-breaking global Hopf bifurcation in memory-based Multi-Agent Systems.

<< ️This (AA) dissertation provides the first systematic study of symmetric consensus-breaking bifurcation to periodic multiconsensus in multi-agent systems. It analyzes this for three classes of multi-agent systems based on three different types of memory, whose closed-loop dynamics equations form delay differential equations of retarded type, neutral type, and pseudoneutral type - a subclassification of retarded type equations introduced in this dissertation which bridges retarded and neutral type delay equations. >>

<< ️Equivariant twisted degree is used to analyze the symmetric global Hopf bifurcation problem in these systems, i.e. bifurcation from a stable consensus to periodic multiconsensus. This shows how the effects of memory allow self-organizing agents to move beyond mere stationary consensus. Theoretical results for the global Hopf bifurcation and symmetric classification of periodic multiconsensus solutions across all three systems are provided, and numerical results are conducted to both validate and enhance the theoretical predictions by providing stability information on the branches which is not obtainable by the degree alone. >>

<< These principles are demonstrated in three real-world applications: one involving the control of formations of UAVs (Unmanned Aerial Vehicles), allowing them to maintain their overall spatial relationships while dancing in complex selectable oscillations; and two more in networked asset markets featuring different traders with different memory-based strategies, showing how similar mechanisms can be responsible for economic cycles of bubbles and crashes. >>

<< Finally, (AA) also numerically investigate resonant double Hopf bifurcations in the neutral delay system, showing strong evidence of a breakdown to chaos via the Ruelle-Takens-Newhouse scenario and the existence of riddled basins. >>

Casey Maikalani Crane. Consensus-Breaking Global Hopf Bifurcation in Memory-Based Multi-Agent Systems. Dissertation. The University of Texas at Dallas. Aug 2026. Supervising Professor: Wieslaw Krawcewicz, Chair.  arXiv: 2607.02388v1 [math.DS]. Jul 2, 2026.

https://arxiv.org/abs/2607.02388

Also: network, swarm, bubble, crack, chaos, transition, dance, in https://www.inkgmr.net/kwrds.html 

Keywords: life, gst, networks, swarm, bubbles, crack, chaos, transitions, dance, multi-agent systems, symmetric consensus-breaking bifurcation, stable consensus, periodic multiconsensus, symmetric global Hopf bifurcation, self-organizing agents, economic cycles of bubbles and crashes, riddled basins. 

# gst: dynamics of coupled stochastic van der Pol oscillators; bifurcations, synchronization and chaos.

<< ️This (AA) work presents a comprehensive analysis of coupled stochastic van der Pol oscillators, a paradigm for understanding synchronization, bifurcations, and chaos in nonlinear systems subject to random fluctuations. The system comprises two or more oscillators with nonlinear damping, linear diffusive coupling, and additive Gaussian white noise. >>

<< ️(AA) develop a unified framework that systematically connects global bifurcations, synchronization phenomena, and chaotic dynamics within a single coherent stochastic model. (They) explore the stochastic dynamics of coupled van der Pol oscillators by seamlessly blending theoretical principles with in-depth numerical simulations. This integrated approach forms a robust framework for analysis, with essential phenomena clearly depicted in the accompanying figures. (AA) then extend this framework to a comprehensive investigation of large networks, focusing on their continuum limit, emergent pattern formation, the role of noise, and the onset of collective chaos. >>

Shenglan Yuan, Xiang Zhou. Dynamics of Coupled Stochastic van der Pol Oscillators: Bifurcations, Synchronization and Chaos.  arXiv: 2606.31445v1 [nlin.CD]. Jun 30, 2026. 

https://arxiv.org/abs/2606.31445v1

Also: chaos, noise, random, disorder & fluctuations, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, noise, randomness, disorder, fluctuations, coupled stochastic van der Pol oscillators, synchronization, bifurcations, emergent pattern formation, collective chaos.

# gst: uncertainty growth in stably stratified turbulence.

<< ️(AA) investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, (They) quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. >>

<< ️At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. (AA) systematically examine how this exponent depends on stratification strength, quantified by the Brunt-Väisälä frequency and the Froude number, in a parameter regime relevant to oceanic flows. >>

<< (They) find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence—initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. >>

<< ️An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. (AA) results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows. >>

Mrinal Jyoti Powdel, Samriddhi Sankar Ray. Uncertainty growth in stably stratified turbulence. Phys. Rev. Fluids 11, 064615. Jun 23, 2026. 

https://journals.aps.org/prfluids/abstract/10.1103/xblr-vpl3

arXiv: 2512.05656v1 [physics.flu-dyn].

https://arxiv.org/abs/2512.05656

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

Keywords: gst, chaos, turbulence, transitions, uncertainty growth, three-dimensional turbulence, stratified turbulence, infinitesimal perturbations, stratification strength, anisotropy. 

# gst: effective synchronization amid noise-induced chaos.

<< ️Two remote agents with synchronized clocks may use them to act in concert and communicate. This necessitates some means of creating and maintaining synchrony. One method, not requiring any direct interaction between the agents, is to expose them to a common, environmental, stochastic forcing. This “noise-induced synchronization” occurs only under sufficiently mild forcing; stronger forcing disrupts synchronization. >>

<< ️(AA) investigate the regime of strong noise, where the clocks' relative phases evolve chaotically. Using a simple realization of disruptive noise, (They) demonstrate effective synchronization. First, although the relative phases of the two clocks varied erratically, (They) confirm that they became statistically independent of initial conditions and hence equivalent after a well-defined timescale. Second, (They) show that an agent can estimate an effective phase that closely agrees with the other's phase. Thus, synchronization is practically attainable beyond the regime of conventional noise-induced synchronization. >>

Benjamin Sorkin, Thomas A. Witten. Effective synchronization amid noise-induced chaos. Phys. Rev. E 113, 054215. May 19, 2026.

https://journals.aps.org/pre/abstract/10.1103/rqgs-99d9

arXiv: 2505.08942v3 [cond-mat.stat-mech]. Feb 22, 2026.

https://arxiv.org/abs/2505.08942

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

Keywords: gst, noise, chaos, transitions, noise-induced transitions, noise-induced synchronization, noise-induced chaos, synchronization transition, kick, kicked trajectory.

# gst: describing a universal critical behavior in a transition from order to chaos.

<< ️(AA) present a comprehensive discussion of a transition from integrability to nonintegrability in an oval billiard with a static boundary. This transition is controlled by a deformation parameter 𝜀, which modifies the boundary shape from circular, corresponding to 𝜀=0 and an integrable dynamics, to oval for 𝜀≠0, where nonintegrability emerges. >>

<< ️The deformation of the circular billiard gives rise to a chaotic layer that develops along a well-defined stripe in phase space. By introducing a set of transformations that isolate this chaotic stripe, (They) characterize the diffusive spreading of ensembles of trajectories and identify an observable, 𝜔_(rms,sat), which plays the role of an order parameter for the transition. >>

<< For small deformations, the saturation value of the diffusion obeys the scaling law 𝜔_(rms,sat)∝𝜀^(˜𝛼), with a critical exponent ˜𝛼=0.507⁢(2), vanishing continuously as 𝜀→0. The associated susceptibility, 𝜒=𝑑⁢𝜔_(rms,sat)/𝑑⁢𝜀, diverges in the same limit, signaling the presence of critical behavior analogous to that observed in second-order (continuous) phase transitions in statistical mechanics. >>

Edson D. Leonel, Mayla A. M. de Almeida, Juan Pedro Tarigo, et al. Describing a universal critical behavior in a transition from order to chaos. Phys. Rev. E 113, 054220. May 28, 2026.

https://journals.aps.org/pre/abstract/10.1103/7231-j7zv

arXiv: 2602.17810v1 [nlin.CD]. Feb 19, 2026.

https://arxiv.org/abs/2602.17810

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

Keywords: gst, billiard, oval billiard, transitions, order, disorder, elementary excitations, small deformations, topological defects, criticality, chaotic stripes, chaos.

# gst: spin-hair induced chaos of spinning test particles in rotating hairy black holes.

<< ️(AA) investigate the finite-time instability of massive spinning test particles around a rotating hairy black hole generated through gravitational decoupling. (They) show that spin–curvature coupling and the hairy geometry can shift the evolved orbit away from the requested seed parameters, making the empirical orbital map essential for interpreting the dynamics. >>

<< Small-spin and geodesic trajectories remain close to regular behavior, whereas large-spin trajectories show stronger finite-time growth. A scan of the (S,β) plane shows that the instability does not grow monotonically, but appears in localized regions where the particle spin and the radial profile of the hair act cooperatively. Thus, the hairy background does not simply rescale the Kerr result; it reorganizes the strong-field phase-space region sampled by spinning particles. >>

Surojit Dalui, Xian-Hui Ge. Spin-Hair Induced Chaos of Spinning Test Particles in Rotating Hairy Black Holes. arXiv: 2605.19673v1 [gr-qc]. May 19, 2026.

https://arxiv.org/abs/2605.19673

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

Keywords: gst, black hole, instability, particle, chaos, rotating hairy black hole.

# gst: from chaos to synchrony in recurrent excitatory-inhibitory networks with target-specific inhibition.

<< ️Biological neural networks can operate in qualitatively distinct dynamical regimes, and transitions between these regimes are thought to underlie changes in computation and behavior. The seminal work of Sompolinsky, Crisanti, and Sommers (SCS) showed that random recurrent networks undergo a transition from quiescence to asynchronous chaos, establishing a paradigmatic link between random connectivity, dynamical instability, and internally generated fluctuations in neural circuits. >>

<< ️Here, (AA) extend this framework to two-population firing-rate networks with segregated excitatory and inhibitory neurons and target-specific inhibitory couplings that break excitation--inhibition balance. Using dynamical mean-field theory, (They) derive self-consistent equations for the macroscopic mean activities and autocorrelations, together with stability criteria distinguishing mean-driven and fluctuation-driven instabilities. (They) show that target-specific inhibition organizes the phase diagram into three qualitative classes: inhibition-dominated or strictly balanced networks display only quiescent activity and asynchronous chaos; excitation-dominated networks display persistent activity together with either synchronous chaos with non-vanishing mean activity or coherent oscillations, depending on the stability-matrix eigenvalues. >>

<< Crucially, coherent oscillations do not coexist with chaotic fluctuations around the periodic mean trajectory; rather, their onset suppresses the chaotic component, reminiscent of input-induced suppression of chaos. These results generalize SCS theory to recurrent networks with explicit excitatory--inhibitory structure and identify target-specific inhibition as a key control parameter for large-scale neural dynamics. >>

Carles Martorell, Rubén Calvo, Alessia Annibale, et al. From Chaos to Synchrony in Recurrent Excitatory-Inhibitory Networks with Target-Specific Inhibition. arXiv: 2605.14916v1 [cond-mat.dis-nn]. May 14, 2026.

https://arxiv.org/abs/2605.14916

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

Keywords: gst, networks, fluctuations, instability, transitions, chaos, biological neural networks, random recurrent networks, asynchronous chaos, excitation--inhibition balance, target-specific inhibition.

# gst: critical parameters of an oval billiard with an elliptical component.

<< ️(AA) explore the critical parameters responsible for the transition from integrability to chaos in a family of billiards combining elliptical and oval deformations. Unlike standard oval billiards, where a known critical parameter governs the destruction of the last invariant curve, the introduction of an integrable elliptic component yields a second deformation axis. >>

<< (They) derive an analytical expression for the critical parameter in this combined system and validate it numerically using Slater's theorem, showing that increasing the elliptical component lowers the critical threshold for global chaos. >>

<< ️Moreover, (They) uncover a previously unexplored regime: when the two deformation components are in phase, the elliptic contribution progressively suppresses chaos, leading to the restoration of invariant curves and periodic orbits. A first-order analytical approximation confirms this behavior, supported by numerical validation. >>

<< ️(Their) results reveal how the interplay between distinct boundary deformations enriches phase-space organization and offers enhanced controllability of chaotic dynamics in billiard systems. >>

Anne Kétri P. da Fonseca, Joelson D. V. Hermes, Edson D. Leonel. Critical parameters of an oval billiard with an elliptical component. arXiv: 2605.00145v1 [nlin.CD]. Apr 30, 2026. 

https://arxiv.org/abs/2605.00145

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

Keywords: gst, billiard, transition, chaos, criticality, elliptical and oval deformations.