# gst: apropos of Parrondo paradox, controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware

<< ️Advancements in noisy intermediate-scale quantum (NISQ) computing are steadily pushing these systems toward outperforming classical supercomputers on specific well-defined computational tasks. In this work (AA) explore and control quantum chaos in NISQ systems using discrete-time quantum walks (DTQWs) on cyclic graphs. To efficiently implement quantum walks on NISQ hardware, (They) employ the quantum Fourier transform to diagonalize the conditional shift operator, optimizing circuit depth and fidelity. >>

<< ️(AA) experimentally realize the transition from quantum chaos to order via DTQW dynamics on both odd and even cyclic graphs, specifically 3- and 4-cycle graphs, using the counterintuitive Parrondo paradox strategy across three different NISQ devices. >>

<< ️While the 4-cycle graphs exhibit high-fidelity quantum evolution, the 3-cycle implementation shows significant fidelity improvement when augmented with dynamical decoupling pulses. (Their) results demonstrate a practical approach to probing and harnessing controlled chaotic dynamics on real quantum hardware, laying the groundwork for future quantum algorithms and cryptographic protocols based on quantum walks. >>

Aditi Rath, Dinesh Kumar Panda, Colin Benjamin. Controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware. Phys. Rev. E 112, 054219. Nov 18, 2025.

https://journals.aps.org/pre/abstract/10.1103/m89r-2dy5

arXiv: 2506.11225v2 [quant-ph]. Nov 4, 2025.

https://arxiv.org/abs/2506.11225

Also: parrondo, noise, walk, walking, order, chaos, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, parrondo, noise, walk, walking, quantum walk, order, chaos, quantum chaos, transition, dynamical decoupling pulses, cryptography.

# gst: turbulence at low Reynolds numbers.

<< ️Turbulence -- ubiquitous in nature and engineering alike  -- is traditionally viewed as an intrinsically inertial phenomenon, emerging only when the Reynolds number (Re), which quantifies the ratio of inertial to dissipative forces, far exceeds unity. >>

<< ️Here, (AA) demonstrate that strong energy flux between different length scales of motion -- a defining hallmark of turbulence -- can persist even at Re ~ 1, thereby extending the known regime of turbulent flows beyond the classical high-Re paradigm. (They) show that scale-to-scale energy transfer can be recast as a mechanical process between turbulent stress and large-scale flow deformation. >>

<< ️In quasi-two-dimensional (quasi-2D) flows driven by electromagnetic forcing, (They) introduce directionally biased perturbations that enhance this interaction, amplifying the spectral energy flux by more than two orders of magnitude, even in the absence of dominant inertial forces. >>

<< ️This (AA) study establishes a new regime of 2D Navier-Stokes (N-S) turbulence, challenging long-standing assumptions about the high Re conditions required for turbulent flows. Beyond revising classical belief, (Their) results offer a generalizable strategy for engineering multiscale transport in flows that lack inertial dominance, such as those found in microfluidic and low-Re biological systems. >>

Ziyue Yu, Xinyu Si, Lei Fang. Turbulence at Low Reynolds Numbers. arXiv: 2511.05800v1 [physics.flu-dyn]. Nov 8, 2025.

https://arxiv.org/abs/2511.05800

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

Keywords: gst, turbulence, chaos,  transitions.

# gst: apropos of itinerant behaviors, from chaotic itinerancy to intermittent synchronization in complex networks.

<< ️Although synchronization has been extensively studied, important processes underlying its emergence have remained hidden by the use of global order parameters. Here, (AA) uncover how the route unfolds through a sequential transition between two well-known but previously unconnected phenomena: chaotic itinerancy (CI) and intermittent synchronization (IS). >>

<< ️Using a new symbolic dynamics, (They) show that CI emerges as a collective yet unsynchronized exploration of different domains of the high-dimensional attractor, whose dimension is reduced as the coupling increases, ultimately collapsing back into the reference chaotic attractor of an individual unit. At this stage, the IS can emerge as irregular alternations between synchronous and asynchronous phases. The two phenomena are therefore mutually exclusive, each dominating a distinct coupling interval and governed by different mechanisms. >>

<< ️Network structural heterogeneity enhances itinerant behavior since access to different domains of the attractor depends on the nodes' topological roles. The CI--IS crossover occurs within a consistent coupling interval across models and topologies. Experiments on electronic oscillator networks confirm this two-step process, establishing a unified framework for the route to synchronization in complex systems. >>

I. Leyva, Irene Sendiña-Nadal, Christophe Letellier, et al. From chaotic itinerancy to intermittent synchronization in complex networks. arXiv: 2511.09253v1 [nlin.AO]. Nov 12, 2025.

https://arxiv.org/abs/2511.09253

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

Keywords: gst, networks, behavior, intermittency, transitions, attractor, chaos, collapse, chaotic itinerancy, intermittent synchronization, structural heterogeneity, itinerant behavior.

# gst: effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop.

<< ️The introduction of stochastic forcing to dynamical systems has been shown to induce qualitatively different behaviors, such as attractor hopping, to otherwise stable systems as they approach bifurcation. In this (AA) study, the effect of stochastic forcing on systems that have already undergone bifurcation and evolve on a chaotic attractor is explored. Markov and state-independent models of turbulence-induced stochasticity are developed, and their effects on a natural circulation loop operating in the chaotic regime are compared. >>

<< ️Stochasticity introduces considerable uncertainty into the duration of the initial chaotic transient but tends to accelerate it on average. An Ornstein-Uhlenbeck model of turbulent fluctuations is shown to produce results equivalent to a bootstrapped raw direct numerical simulation signal. >>

<< Similar, though less pronounced, effects are found for systems operating in the chaotic itinerant regime. The Markov model of chaotic itinerancy which is typically applied to this class of problems is shown to be invalid for this system and the Lorenz system, to which it has been applied in the past. >>

<< ️Off-discrete transitions and an upper limit on the time between flow reversals are explained by near misses of the attractor ruins caused by lingering excitation of high-order modes during chaotic itinerancy. >>

John Matulis, Hitesh Bindra. Effect of stochasticity on initial transients and chaotic itinerancy for a natural circulation loop. Phys. Rev. E 112, 044223. Oct 23, 2025

https://journals.aps.org/pre/abstract/10.1103/42pn-wttx

Also: disorder & fluctuations, turbulence, attractor, chaos, transition, uncertainty, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, disorder, fluctuations, turbulence, attractor, chaos, transition, uncertainty, stochasticity, flow instability, chaotic itinerancy, noise-induced transitions.

# gst: implementation of a generalized intermittency scenario in the Rossler dynamical system.

<< The realization of novel scenario involving transitions between different types of chaotic attractors is investigated for the Rossler system. Characteristic features indicative of the presence of generalized intermittency scenario in this system are identified. The properties of "chaos-chaos" transitions following the generalized intermittency scenario are analyzed in detail based on phase-parametric characteristics, Lyapunov characteristic exponents, phase portraits, and Poincare sections. >>

O.O. Horchakov, A.Yu. Shvets. Implementation of a generalized intermittency scenario in the Rossler dynamical system. arXiv: 2511.03364v1 [nlin.CD]. Nov 5, 2025.

https://arxiv.org/abs/2511.03364

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

Keywords: gst, intermittency, attractors, chaos, transitions, chaos-chaos transitions.

# gst: energy transport and chaos in a one-dimensional disordered nonlinear stub lattice

<< ️(AA) investigate energy propagation in a one-dimensional stub lattice in the presence of both disorder and nonlinearity. In the periodic case, the stub lattice hosts two dispersive bands separated by a flat band; however, (They) show that sufficiently strong disorder fills all intermediate band gaps. By mapping the two-dimensional parameter space of disorder and nonlinearity, (AA) identify three distinct dynamical regimes (weak chaos, strong chaos, and self-trapping) through numerical simulations of initially localized wave packets. >>

<< ️When disorder is strong enough to close the frequency gaps, the results closely resemble those obtained in the one-dimensional disordered discrete nonlinear Schrödinger equation and Klein-Gordon lattice model. In particular, subdiffusive spreading is observed in both the weak and strong chaos regimes, with the second moment m_2 of the norm distribution scaling as m_2 ∝ t^0.33 and m_2 ∝ t^0.5, respectively. The system’s chaotic behavior follows a similar trend, with the finite-time maximum Lyapunov exponent Λ decaying as Λ ∝ t^−0.25 and Λ ∝ t^−0.3. For moderate disorder strengths, i.e., near the point of gap closing, (They) find that the presence of small frequency gaps does not exert any noticeable influence on the spreading behavior. >>

<< ️(AA) findings extend the characterization of nonlinear disordered lattices in both weak and strong chaos regimes to other network geometries, such as the stub lattice, which serves as a representative flat-band system. >>

Su Ho Cheong, Arnold Ngapasare, et al. Energy transport and chaos in a one-dimensional disordered nonlinear stub lattice. arXiv: 2511.04159v1 [nlin.CD].  Nov 6, 2025.

https://arxiv.org/abs/2511.04159

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

Keywords: gst, networks, waves, disorder, chaos, stub lattice, subdiffusive spreading.

# gst: dynamical phase transitions across slow and fast regimes in a two-tone driven Duffing resonator

<< In this work, (AA) established an analytical framework to describe dynamical phase transitions in a Duffing resonator under bichromatic driving. (They) reveal two regimes: a slow-beating one, where the secondary tone slowly modulates the main drive and can push the system past bifurcations, and a fast-modulation one. >>

<< (AA) analysis shows that even a weak secondary tone can profoundly reshape the dynamics, inducing transitions between coexisting attractors that cannot be explained by perturbative treatments of the secondary tone. >>

<< This provides a qualitative yet predictive tool to detect and categorize different types of dynamical phase transitions in two-tone driven nonlinear systems. >>

Soumya S. Kumar, Javier del Pino, et al. Dynamical Phase Transitions Across Slow and Fast Regimes in a Two-Tone Driven Duffing Resonator. arXiv: 2511.01985v1 [cond-mat.mes-hall]. Nov 3, 2025.

https://arxiv.org/abs/2511.01985

 

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

Keywords: gst, attractor, transitions, chaos,  Duffing resonator, bichromatic driving. 

# gst: transition to chaos with conical billiards.

<< ️In this paper, (AA) introduced and extensively investigated dynamical billiards on the surface of a cone with a tilted base. Upon varying the cone angle β, corresponding to a deficit angle 

2πχ = 2π(1 − sin(β)), and tilt angle γ, (They) identified three distinct types of trajectories with associated Poincaré map for conical billiards: rim, hourglass, and mixed. >>

<< ️Region I, where Poincaré space consists of rim, hourglass, and mixed trajectories; Region IIB, where Poincaré space consists of only hourglass and mixed trajectories; and Region IIA, in which (They) find choices of γ and χ for which almost all trajectories are strongly mixing. (..) (AA) also developed a scheme for identifying strongly mixing trajectories. >>

<< ️Furthermore, (They) were able to show that a dynamical billiard on a surface with exclusively convex and positive Gaussian curvature in three dimensions can still exhibit ergodic behavior in certain parameter regimes. >>

<< ️A particularly intriguing feature of this system is that by tuning χ and γ, nearly all points in (θ,ϕ) Poincaré space describing conical line segments in between bounces can be placed at the edge between chaotic and integrable dynamics. Thus this work highlights the potential of conical billiards as a model system for exploring intriguing problems inspired by neural networks at the “edge of chaos”. >>

Lara Braverman, David R. Nelson. Transition to chaos with conical billiards. arXiv: 2508.02786v1 [nlin.CD]. Aug 4, 2025. 

https://arxiv.org/abs/2508.02786

Phys. Rev. E 112, 044221. Oct 21, 2025.

https://journals.aps.org/pre/abstract/10.1103/18f7-sqhz

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

Keywords: gst, billiards, conical billiard, chaos, transitions, neural networks

# gst: nonreciprocity induced spatiotemporal chaos: reactive vs dissipative routes.

<< ️Nonreciprocal interactions fundamentally alter the collective dynamics of nonlinear oscillator networks. Here (AA) investigate Stuart-Landau oscillators on a ring with nonreciprocal reactive or dissipative couplings combined with Kerr-type or dissipative nonlinearities. >>

<< ️Through numerical simulations and linear analysis, (They) uncover two distinct and universal pathways by which enhanced nonreciprocity drives spatiotemporal chaos. Nonreciprocal reactive coupling with Kerr-type nonlinearity amplifies instabilities through growth-rate variations, while nonreciprocal dissipative coupling with Kerr-type nonlinearity broadens eigenfrequency distributions and destroys coherence, which, upon nonlinear saturation, evolve into fully developed chaos. In contrast, dissipative nonlinearities universally suppress chaos, enforcing bounded periodic states. >>

<< ️(AA) findings establish a minimal yet general framework that goes beyond case-specific models and demonstrate that nonreciprocity provides a universal organizing principle for the onset and control of spatiotemporal chaos in oscillator networks and related complex systems. >>

Jung-Wan Ryu. Nonreciprocity induced spatiotemporal chaos: Reactive vs dissipative routes. arXiv: 2509.20992v1 [nlin.CD]. Sep 25, 2025

https://arxiv.org/abs/2509.20992

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

Keywords: gst, networks, instability, chaos, nonreciprocity, nonreciprocal interactions, nonreciprocal reactive-- dissipative couplings.

# gst: extreme vertical drafts as drivers of Lagrangian dispersion in stably stratified turbulent flows.

<< ️The dispersion of Lagrangian particle pairs is a fundamental process in turbulence, with implications for mixing, transport, and the statistical properties of particles in geophysical and environmental flows. While classical theories describe pair dispersion through scaling laws related to energy cascades, extreme events in turbulent flows can significantly alter these dynamics. This is especially important in stratified flows, where intermittency manifests itself also as strong updrafts and downdrafts. >>

<< ️In this study, (AA) investigate the influence of extreme events on the relative dispersion of particle pairs in stably stratified turbulence. Using numerical simulations (They) analyze the statistical properties of pair separation across different regimes, and quantify deviations from classical Richardson scaling. (Their) results highlight the role of extreme drafts in accelerating dispersion. >>

Christian Reartes, Pablo D. Mininni, Raffaele Marino. Extreme vertical drafts as drivers of Lagrangian dispersion in stably stratified turbulent flows. arXiv: 2509.12962v1 [physics.flu-dyn]. Sep 16, 2025.

https://arxiv.org/abs/2509.12962

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

Keywords: gst, turbulence, stratified turbulence,  intermittency, chaos, transitions, particles, extreme events, stratified flows, accelerating dispersion.

# gst: spiral defect chaos with intermittency increases mean termination time

<< ️Cardiac models are examples of excitable systems and can support stable spiral waves. For certain parameter values, however, these spiral waves can become unstable, resulting in spiral defect chaos (SDC), characterized by the continuous creation and annihilation of spiral waves and thought to underlie atrial fibrillation. During SDC, the number of spiral waves fluctuates and drops to zero at termination. >>

<< ️In this work, (AA) demonstrate that varying a single parameter allows the system to transition from SDC to a single spiral wave, passing through an intermediate regime of intermittency. In such intermittent dynamics, intervals of SDC are sandwiched between non-SDC intervals during which the number of spiral waves remains small and constant. (They) quantify this intermittency and show that the mean termination time increases significantly as the control parameter approaches values for which a single spiral wave is stable. >>

<<  In addition, (AA) observe that quasistable spiral waves may intermittently persist in part of the computational domain, while the rest of the domain exhibits SDC. >> 

Mahesh Kumar Mulimani, Wouter-Jan Rappel. Spiral defect chaos with intermittency increases mean termination time. Phys. Rev. E 112, 034203. Sep 3, 2025.

https://journals.aps.org/pre/abstract/10.1103/bwpl-qqyl

arXiv: 2505.06427v1 [nlin.CD]. May 9,  2025

https://arxiv.org/abs/2505.06427

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

Keywords: gst, waves, spiral & scroll waves, intermittency, vortex, chaos, spiral defect chaos.

# ecol: stabilization of macroscopic dynamics by fine-grained disorder in many-species ecosystems.

<< ️Models for complex, heterogeneous systems such as ecological communities vary in the level of organization they describe. When the dynamics at the species level is unknown, one typically resorts to heuristic "macroscopic" models that capture relationships among a few degrees of freedom, e.g., groups of similar species, and commonly display out-of-equilibrium dynamics. These models, however, exactly reflect the species-level "microscopic" dynamics only when microscopic heterogeneity can be neglected. >>

<< ️Here, (AA) address the robustness of such macroscopic descriptions to the addition of disordered microscopic interactions. While disorder is known to destabilize equilibria at the microscopic level, leading to asynchronous (typically chaotic) fluctuations, (They) show that it can also stabilize synchronous species fluctuations driven by macroscopic structure. >>

<< ️(AA) analytically find the conditions for the existence of heterogeneity-stabilized equilibria and relate their stability to a mismatch in the time scales of individual species. This may shed light on the empirical observation that many-species ecosystems often appear stable despite highly diverse and potentially destabilizing interactions between species and functional groups. >>

Juan Giral Martínez, Silvia De Monte, Matthieu Barbier. Stabilization of macroscopic dynamics by fine-grained disorder in many-species ecosystems. Phys. Rev. E 112, 034305. Sep 4, 2025.

https://journals.aps.org/pre/abstract/10.1103/5w5x-b1c2

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

Keywords: gst, disorder, disorder & fluctuations, chaos, ecological communities, disordered microscopic interactions, asynchronous fluctuations, heterogeneity-stabilized equilibria.

# gst: a journey into billiard systems

<< ️Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these simple rules, billiard systems can produce remarkably rich behaviors: some table shapes generate regular, periodic patterns, while others give rise to complete chaos. >>

<< Scientists also study what happens when (They) shrink the ball down to the size of an electron to a world where quantum effects take over and the familiar reflection rules no longer apply. >>

<< ️In this article, (AA) discuss billiard systems in their many forms and show how such a simple setup can reveal fundamental insights into the behavior of nature at both classical and quantum scales. >>

Weiqi Chu, Matthew Dobson. What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems. arXiv: 2508.18519v1 [math.DS]. Aug 25, 2025.

https://arxiv.org/abs/2508.18519

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

Keywords: gst, billiard, transition, chaos.

# brain: spontaneous emergence of metacognition in neuronal computation.

<< ️Metacognition, a hallmark of human intelligence, enables individuals to assess prediction uncertainty, providing an advantage over artificial intelligence in anticipating risks and performing tasks that demand trustworthiness and reliability. >>

<< ️Here, (AA) demonstrate that metacognition can naturally emerge in recurrent neural networks trained on cognitive tasks without guidance from any probabilistic inference rules or additional network architectures. Through naturally embedded nonlinear coupling with the mean of the network output, the covariance of the network output engages in metacognition by assessing the uncertainty associated with the mean, which represents the task responses. >>

<< ️(AA) further propose testable predictions about how key features of neuronal computation in the brain—noise, neuronal correlations, and heterogeneity—contribute to metacognition. >>

Hengyuan Ma, Wenlian Lu, Jianfeng Feng. Spontaneous emergence of metacognition in neuronal computation. Phys. Rev. Research 7, 033188. Aug 22, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/f1hv-bf1f

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

Keywords: gst, brain, cognition, metacognition, learning, memory, networks, biological neural networks, biological information processing, decision making, uncertainty, stochasticity, noise, chaos.

# gst: hidden qu-classical correspondence in chaotic billiards revealed by mutual information.

<< ️Avoided level crossings, commonly associated with quantum chaos, are typically interpreted as signatures of eigenstate hybridization and spatial delocalization, often viewed as ergodic spreading. >>

<< ️(AA) show that, contrary to this expectation, increasing chaos in quantum billiards enhances mutual information between conjugate phase space variables, revealing nontrivial correlations. Using an information-theoretic decomposition of eigenstate entropy, (They) demonstrate that spatial delocalization may coincide with increased mutual information between position and momentum. >>

<< These correlations track classical invariant structures in phase space and persist beyond the semiclassical regime, suggesting a robust information-theoretic manifestation of quantum-classical correspondence. >>

Kyu-Won Park, Soojoon Lee, Kabgyun Jeong. Hidden quantum-classical correspondence in chaotic billiards revealed by mutual information. Phys. Rev. E 112, 024209. Aug 13, 2025.

https://journals.aps.org/pre/abstract/10.1103/qpxx-csdj

arXiv:2505.08205v1 [nlin.CD]. May 13, 2025.

https://arxiv.org/abs/2505.08205

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

Keywords: gst, billiard, chaos, qu-chaos, waves, quantum-to-classical transition

# gst: extreme event precursor prediction in turbulence.

<< ️(AA) present a general framework to predict precursors to extreme events in turbulent dynamical systems. The approach combines phase-space reconstruction techniques with recurrence matrices and convolutional neural networks (CNN) to identify precursors to extreme events. >>

<< ️(They) evaluate the framework across three distinct testbed systems: a triad turbulent interaction model, a prototype stochastic anisotropic turbulent flow, and the Kolmogorov flow. This method offers three key advantages: (1) a threshold-free classification strategy that eliminates subjective parameter tuning, (2) efficient training using only O (100) recurrence matrices, and (3) ability to generalize to unseen systems. >>

<< ️The results demonstrate robust predictive performance across all test systems: 96% detection rate for the triad model with a mean lead time of 1.8 time units, 96% for the anisotropic turbulent flow with a mean lead time of 6.1 time units, and 93% for the Kolmogorov flow with a mean lead time of 22.7 units. >> 

Rahul Agarwal, Mustafa A. Mohamad. Extreme Event Precursor Prediction in Turbulent Dynamical Systems via CNN-Augmented Recurrence Analysis. arXiv: 2508.04301v1 [cs.CE]. Aug 6, 2025.

https://arxiv.org/abs/2508.04301

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

Keywords: gst, turbulence, chaos, extreme events, convolutional neural networks (CNN).

# gst: transition to chaos with conical billiards.

<< ️(AA) adapt ideas from geometrical optics and classical billiard dynamics to consider particle trajectories with constant velocity on a cone with specular reflections off an elliptical boundary formed by the intersection with a tilted plane, with tilt angle γ. >>

<< ️(They) explore the dynamics as a function of γ and the cone deficit angle χ that controls the sharpness of the apex, where a point source of positive Gaussian curvature is concentrated. >>

<< ️(AA) find regions of the (γ,χ) plane where, depending on the initial conditions, either (A) the trajectories sample the entire cone base and avoid the apex region; (B) sample only a portion of the base region while again avoiding the apex; or (C) sample the entire cone surface much more uniformly, suggestive of ergodicity. >>

<< ️The special case of an untilted cone displays only type A trajectories which form a ring caustic at the distance of closest approach to the apex. However, (They) observe an intricate transition to chaotic dynamics dominated by Type (C) trajectories for sufficiently large χ and γ. A Poincaré map that summarizes trajectories decomposed into the geodesic segments interrupted by specular reflections provides a powerful method for visualizing the transition to chaos. (AA) then analyze the similarities and differences of the path to chaos for conical billiards with other area-preserving conservative maps. >>

Lara Braverman, David R. Nelson. Transition to chaos with conical billiards. arXiv: 2508.02786v1 [nlin.CD]. Aug 4, 2025.

https://arxiv.org/abs/2508.02786

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

Keywords: gst, billiard, particles, transitions, chaos. 

# gst: an analysis of the phenomenon of chaotic itinerancy.

AA << introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. (They) determine systems likely to experience chaotic itinerancy by means of local Shannon entropy and local permutation entropy. In such systems, we find quasi-stable states (attractor ruins) and chaotic transition states using a density-based clustering algorithm. >>

Their << ️approach then focuses on examining the chaotic itinerancy dynamics through the characterization of residence times within these states and chaotic transitions between them with the help of some statistical tests. The effectiveness of these methods is demonstrated on two systems that serve as well-known models exhibiting chaotic itinerancy: globally coupled logistic maps (GCM) and mutually coupled Gaussian maps. >>

<< ️Although the phenomenon of chaotic itinerancy is often associated with high dimensional systems, (They) were able to provide evidence for the presence of this phenomenon in the studied low-dimensional systems. >>

Nikodem Mierski, Paweł Pilarczyk. Analysis of the Chaotic Itinerancy Phenomenon using Entropy and Clustering. arXiv: 2507.22643v1 [nlin.CD]. Jul 30, 2025. 

https://arxiv.org/abs/2507.22643

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

Keywords: gst, chaos, intermittency, transitions, chaotic itinerancy, low-dimensional systems.

# gst: irreversibility in scalar active turbulence, the role of topological defects.

<< ️In many active systems, swimmers collectively stir the surrounding fluid to stabilize some self-sustained vortices. The resulting nonequilibrium state is often referred to as active turbulence, by analogy with the turbulence of passive fluids under external stirring. Although active turbulence clearly operates far from equilibrium, it can be challenging to pinpoint which emergent features primarily control the deviation from an equilibrium reversible dynamics. >>

Here, AA << reveal that dynamical irreversibility essentially stems from singularities in the active stress. Specifically, considering the coupled dynamics of the swimmer density and the stream function, (AA) demonstrate that the symmetries of vortical flows around defects determine the overall irreversibility. (Their) detailed analysis leads to identifying specific configurations of defect pairs as the dominant contribution to irreversibility. >>

Byjesh N. Radhakrishnan, Francesco Serafin, et al. Irreversibility in scalar active turbulence: The role of topological defects. arXiv:2507.06073v1 [cond-mat.stat-mech]. Jul 8, 2025.

https://arxiv.org/abs/2507.06073

Also: swim, turbulence, vortex, self-assembly, chaos, clinamen, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, swim, swimmers, turbulence, active turbulence, vortex, self-assembly, chaos, defects, topological defects, deviation, clinamen.

# gst: self-feedback delay induces extreme events in the theoretical Brusselator system.

AA << ️present a study of the theoretical Brusselator model with time-delayed self-feedback, demonstrating its ability to induce extreme events when delays in reaction processes significantly influence subsequent dynamics, with and without diffusion. >>

<< ️Stability analyses reveal the mechanisms driving this behavior with respect to the delay time. The occurrence of extreme events is validated using various numerical and statistical tools, including phase portraits, time series, probability distribution functions, return periods, and spatiotemporal evolution. >>

<< ️A comprehensive two-parameter scan delineates the parameter regimes where the extreme events emerge, alongside the identification of transient chaos within specific regions of the parameter space. To confirm these numerical findings, (AA) constructed an analog electronic circuit that emulates the model, providing experimental validation of the predicted dynamics. >>

S. V. Manivelan, S. Sabarathinam, et al. Self-feedback delay induces extreme events in the theoretical Brusselator system. Phys. Rev. E 112, 014202. Jul 1, 2025.

https://journals.aps.org/pre/abstract/10.1103/v1h2-42w1

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

Keywords: gst, Brusselator system, self-feedback, delay, chaos, transient chaos, transitions, extreme events.