# gst: transient chaos and Rayleigh particle escape out of a time modulated optical trap.

<< ️(AA) consider Rayleigh particles in a periodically modulated optical trap formed by two counterpropagating Gaussian beams. It is shown that for certain values of the parameters the system exhibits transient chaos which manifests itself in particle acceleration and subsequent directional ejection out of the trap. The escape flights are terminated at a distance of hundreds of wavelengths from the trap center and the particles return to the trap under the action of the Stokes force. The particle escape is shown to be a threshold effect that can be potentially employed for particle sorting. >>

Evgeny N. Bulgakov, Konstantin N. Pichugin, Dmitrii N. Maksimov. Transient chaos and Rayleigh particle escape out of a time modulated optical trap. Phys. Rev. E 113, 044216. Apr 23, 2026.

https://journals.aps.org/pre/abstract/10.1103/fj7q-vm5b

arXiv:2512.03403v1 [nlin.CD]. Dec 3, 2025.

https://arxiv.org/abs/2512.03403

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

Keywords: gst, chaos, transitions, particle, escape, periodically modulated trap, threshold effect.

# gst: chaotic ghosts in systems with parameter drift; delay and control critical transitions.

<< ️In dynamical systems with a time-dependent parameter, i.e., parameter drift, after crossing a saddle-node bifurcation, the so-called ghost state formed by the disappeared equilibria or periodic orbit can influence transient dynamics, causing a delayed transition. >>

<< ️This phenomenon has been investigated previously. However, the effect of chaotic ghosts on the critical transition in drifting systems has been less studied. In this paper, (AA) explore how chaotic ghosts and drifting rates influence critical transitions from the perspective of the ensemble. >> 

<< ️The (AA) results reveal the mechanism of the delayed transition related to chaos and how trajectories on the initial ensemble composed of a chaotic attractor transition to a qualitatively different object during the drift. In addition, (They) quantify the delayed transition and further find that the delay follows a power-law scaling with respect to the drifting rate. Finally, (AA) show that the critical transition is fully avoided as long as the reversal rate of the parameter exceeds a certain critical rate, even though the bifurcation point has been crossed. >>

Han Su, Denghui Li, Jicheng Duan, et al. Chaotic ghosts in systems with parameter drift: Delay and control critical transitions. Phys. Rev. E 113, 044207. April 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/bdf8-wkpm

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

Keywords: gst, chaos, attractor, transitions, chaotic attractor transition, chaotic ghosts, criticality, critical transitions, bifurcation point, saddle-node bifurcation, ghost state, transient dynamics, delay, delayed transition, drifting rate.

# gst: quantum kicked top; a paradigmatic model

<< ️The quantum kicked top (QKT) is one of the most widely studied models in quantum chaos, providing a minimal yet powerful framework for exploring the relationship between classical nonlinear dynamics and quantum behavior. Unlike many chaotic systems with infinite-dimensional Hilbert spaces, the QKT possesses a finite-dimensional Hilbert space, making it analytically and numerically controllable while still showing a rich dynamical phenomena. >>

<< ️(AA) present a comprehensive introduction to the QKT as a paradigmatic model of quantum chaos. Starting from the classical kicked top, (They) derive the discrete nonlinear map governing the dynamics on the unit sphere and analyze its phase space structure through fixed points, stability analysis, bifurcations and Lyapunov exponents. (They) then discuss the role of symmetries, including rotational and time-reversal symmetry, and how their breaking modifies the dynamics. >>

<< ️By linking classical phase space structures with quantum dynamical indicators, the QKT provides a clear setting to investigate the emergence of chaotic behavior in the semiclassical limit. The chapter, therefore, highlights the quantum kicked top as a bridge between nonlinear classical dynamics, quantum chaos and modern quantum information science. >>

Avadhut V. Purohit, Udaysinh T. Bhosale. Quantum Kicked Top: A Paradigmatic Model. arXiv: 2604.12345v1 [quant-ph]. Apr 14, 2026.

https://arxiv.org/abs/2604.12345

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

Keywords: gst, chaos, entropy, quantum kicked top, quantum chaos, bifurcations, rotational symmetry, time-reversal symmetry, entanglement, qubits, quantum information, entanglement entropy.

# gst: chaos and quantum tunneling.

<< ️In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space are strictly forbidden, and these sets act as dynamical barriers to one another. In quantum mechanics, in contrast, wave effects allow transitions through such dynamical barriers. This process, known as dynamical tunneling, refers to penetration through dynamical barriers in phase space and was first recognized in the early 1980s. Since then, various aspects of dynamical tunneling have been elucidated, significantly advancing our understanding of such a novel quantum phenomenon. >>

<< ️In this article, (AA) provide an overview of several phenomenological perspectives of dynamical tunneling, including chaos-assisted and resonance-assisted tunneling, and also introduce approaches based on classical mechanics extended into the complex domain. In particular, (They) seek to clarify what is meant by the common claim that "chaos leads to an enhancement of the tunneling probability", which is often made when dynamical tunneling is dressed. (They) discuss what regime this refers to and, if such an enhancement occurs, what its likely origin is. >>

Akira Shudo. Chaos and Quantum Tunneling. arXiv: 2604.12926v1 [nlin.CD]. Apr 14, 2026.

https://arxiv.org/abs/2604.12926

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

Keywords: gst, waves, chaos, transitions, dynamical tunneling, chaos-assisted tunneling, resonance-assisted tunneling.

# gst: apropos of escape, Stochastic Web Map; survival probability and escape frequency.

<< ️(AA) study transport and escape in the Stochastic Web Map (SWM), an area-preserving system with phase-space structure controlled by a symmetry parameter q and nonlinearity K. By analyzing the survival probability P_S(n) and escape frequency P_E(lnn), (They) show that in the chaotic regime escape dynamics is governed by a single time scale n_(typ) ∝ K^(−2)h^(2); here h is the size of the escape horizon. Deviations at large K and small h indicate a breakdown of the quasilinear approximation. Then, upon rescaling the time by n_(typ), escape statistics becomes universal, independent of q. These results demonstrate that escape is controlled by global transport rather than symmetry. >>

K. B. Hidalgo-Castro, J. A. Méndez-Bermúdez, Edson D. Leonel. Stochastic Web Map: Survival probability and escape frequency. arXiv: 2603.20888v1 [nlin.CD]. Mar 21, 2026.

https://arxiv.org/abs/2603.20888

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

Keywords: gst, escape, escape horizon, chaos, global transport.

# gst: phase-space organization of the elastic pendulum; chaotic fraction, energy exchanges, and the order-chaos-order transition.

<< ️(AA) study the phase-space organization of the planar elastic pendulum as a function of its two dimensionless control parameters: the reduced energy R and the squared frequency ratio µ. By randomly sampling the isoenergetic volume to classify trajectories as oscillatory, rotational, or chaotic across the (µ,R) parameter plane, (They) obtain a global portrait of the coexistence and competition between dynamical regimes. >>

<< ️The chaotic fraction is not uniformly distributed across the parameter plane but concentrates in a well-defined central cloud whose ridge follows a linear relation in the (µ,R) plane and whose maximum does not exceed 70% of the available phase space. The order-chaos-order transition is not a global property of the parameter plane but occurs specifically in the central region surrounding this cloud: along paths that traverse it, oscillatory orbits progressively give way to chaotic trajectories, which in turn yield to rotational orbits as the energy grows, revealing a clear sequential mechanism underlying the transition. >> 

<< ️The onset of rotational motion is gradual rather than sharp, reflecting a strong dependence on initial conditions. By decomposing the total energy into spring-like, pendulum-like, and coupling contributions, (They) establish a direct correspondence between the coupling power and the abundance of chaotic trajectories, showing that enhanced inter-mode energy exchange is a reliable indicator of dynamical complexity. >>

Juan P. Tarigo, Cecilia Stari, Edson D. Leonel, et al. Phase-space organization of the elastic pendulum: chaotic fraction, energy exchanges, and the order-chaos-order transition. arXiv: 2604.01503v1 [nlin.CD]. Apr 2, 2026.

https://arxiv.org/abs/2604.01503

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

Keywords: gst, pendulum, planar elastic pendulum, rotation, rotational motion, chaos, transitions, order-chaos-order transition. 

# gst: apropos of ab.normal criticalities, a hypothetical scenario of non-normal route to chaos.

<< ️Deterministic chaos is commonly associated with spectral criticality: exponential sensitivity is expected when Jacobian eigenvalues exceed unity in parts of the attractor, producing the local expansion that offsets contraction elsewhere. (AA) show that this paradigm is incomplete in dimensions d>1.  >>

<< ️(They) construct a bounded 3D dynamical system whose Jacobian is pointwise spectrally contracting, namely all instantaneous eigenvalues remain strictly inside the stability region, yet the system develops a positive maximal Lyapunov exponent and undergoes a transition to chaos as a non-normality index increases at fixed spectral radius. The mechanism relies on the repeated regeneration of transient non-normal amplification through endogenous switching that reinjects trajectories into amplifying non-orthogonal directions. >>

<< ️Although demonstrated here for a discrete-time map, the mechanism is geometric and applies more broadly to deterministic dynamical systems. These results show that chaos can emerge without spectral criticality and identify non-normality as an independent route to deterministic chaos. >>

D. Sornette, V.R. Saiprasad, V. Troude. Non-Normal Route to Chaos. arXiv: 2603.08191v1 [nlin.CD]. Mar 9, 2026.

https://arxiv.org/abs/2603.08191

Also:  Virgile Troude, Sandro Claudio Lera, Ke Wu, Didier Sornette. Illusions of Criticality: Crises Without Tipping Points. arXiv: 2412.01833v5 [nlin.CD]. Oct 3, 2025. https://arxiv.org/abs/2412.01833

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

Keywords: gst, chaos, criticality, transitions, non-normality, transient non-normality, reinjection via endogenous switch.

# gst: localization of information driven by stochastic resetting.

<< ️The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with stochastic resetting drives a sharp dynamical phase transition: (AA) show that the Lyapunov spectrum, i.e., the complete set of Lyapunov exponents, abruptly collapses to zero above a critical resetting rate. >>

<< ️At criticality, (They) find a sudden loss of analyticity of the velocity-dependent Lyapunov exponent, which (They) relate to the transition from ballistic scrambling of information to an arrested regime where information becomes exponentially localized over a characteristic length diverging at criticality with an exponent 𝜈=1/2 and a dynamical exponent 𝑧=2. (They) illustrate (Their) analytical results on generic chaotic dynamics by numerical simulations of coupled map lattices. >>

Camille Aron, Manas Kulkarni. Localization of information driven by stochastic resetting. Phys. Rev. E 113, L022101. Feb 23, 2026.

https://journals.aps.org/pre/abstract/10.1103/pkgb-mp8s

arXiv:2510.07394v2 [cond-mat.stat-mech]. Feb 24, 2026.

https://arxiv.org/abs/2510.07394

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

Keywords: gst, chaos, transition, collapse, randomness, stochasticity, stochastic resetting, phase transition, criticality, critical resetting rate, ballistic scrambling of information.

# gst: a phase description of mutually coupled chaotic oscillators.

<< ️The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally modeled as coupled phase oscillators under weak coupling. This simple representation enables direct inference of inter-rhythm coupling functions from measured time-series data. >>

<< ️However, strongly rhythmic chaos can masquerade as noisy limit cycles. In such cases, standard estimators still return plausible coupling functions even though a phase-oscillator model lacks a priori justification. >>

<< ️(AA) therefore extend the phase description to the chaotic oscillators. Specifically, (They) derive a closed equation for the phase difference by defining the phase on a Poincaré section and averaging the phase dynamics over invariant measures of the induced return maps. Numerically, the derived theoretical functions are in close agreement with those inferred from time-series data. Consequently, (Their) results justify the applicability of phase description to coupled chaotic oscillators and show that data-driven coupling functions retain clear dynamical meaning in the absence of limit cycles. >>

Haruma Furukawa, Takashi Imai, Toshio Aoyagi. A Phase Description of Mutually Coupled Chaotic Oscillators. arXiv: 2602.17519v1 [nlin.CD]. Feb 19, 2026.

https://arxiv.org/abs/2602.17519

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

Keywords: gst, chaos, synchronization of rhythms, limit cycles, noisy limit cycles, coupled phase oscillators, transitions.

# gst: beyond interpolation toward invention, the hypothesis of selective imperfection as a generative framework for analysis, creativity and discovery.

<< ️(AA) introduce materiomusic as a generative framework linking the hierarchical structures of matter with the compositional logic of music. Across proteins, spider webs and flame dynamics, vibrational and architectural principles recur as tonal hierarchies, harmonic progressions, and long-range musical form. >>

<< ️(They) show how sound functions as a scientific probe, an epistemic inversion where listening becomes a mode of seeing and musical composition becomes a blueprint for matter. >>

<< ️Selective imperfection provides the mechanism restoring balance between coherence and adaptability. >>

<< ️(They) show how swarm-based AI models compose music exhibiting human-like structural signatures such as small-world connectivity, modular integration, long-range coherence, suggesting a route beyond interpolation toward invention. (They) show that science and art are generative acts of world-building under constraint, with vibration as a shared grammar organizing structure across scales. >>

Markus J. Buehler. Selective Imperfection as a Generative Framework for Analysis, Creativity and Discovery. arXiv: 2601.00863v1 [cs.LG]. Dec 30,  2025.

https://arxiv.org/abs/2601.00863

Also: jazz, music, clinamen, chaos, defect, error, mistake, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, jazz, music, clinamen, parenklisis, selective imperfection, defect, error, mistake, noise, invention, long-range coherence, chaos.

FonT:  apropos of 'selective imperfection', at one time I was surprised by the structure of a temple gate in Kyoto where one of the elements is installed upside down.

# gst: noise enables conditional recovery from collapse.

<< ️(AA) report a paradoxical phenomenon where stochasticity reverses deterministic collapse in threshold-activated systems. By using a hybrid logistic-sigmoidal map, (They) show that weak noise alters phase-space topology, enabling probabilistic recovery from extinction. Lyapunov and quasipotential analyses reveal noise-induced metastability and stochastic robustness absent in deterministic frameworks. These results suggest that environmental variability can stabilize nonlinear systems, offering a counternarrative to classical extinction theory. >>

Vinesh Vijayan, B. Priyadharshini, R. Sathish Kumar, G. Janaki. Noise enables conditional recovery from collapse: Probabilistic persistence in threshold-activated systems. Phys. Rev. E 112, 064212. Dec 19, 2025.

https://journals.aps.org/pre/abstract/10.1103/xgq1-nnqb

Also:  Vinesh Vijayan, et al. Noise reinstates collapsed populations; stochastic reversal of deterministic extinction. arXiv: 2507.03954v1 [q-bio.PE]. Jul 5, 2025. https://arxiv.org/abs/2507.03954   https://flashontrack.blogspot.com/2025/07/gst-noise-reinstates-collapsed.html

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

Keywords: gst, chaos, chaotic systems, noise, weakness, disorder,  fluctuations, tipping point, transitions, stochasticity, stochastic reversal, stochastic rescue. 

# gst: chaos and regularity in an anisotropic soft squircle billiard.

<< ️A hard-wall billiard is a mathematical model describing the confinement of a free particle that collides specularly and instantaneously with boundaries and discontinuities. Soft billiards are a generalization that includes a smooth boundary whose dynamics are governed by Hamiltonian equations and overcome overly simplistic representations. >>

<< ️(AA) study the dynamical features of an anisotropic soft-wall squircle billiard. This curve is a geometric figure that seamlessly blends the angularity of a square with the smooth curves of a circle. (They) characterize the billiard's emerging trajectories, exhibiting the onset of chaos and its alternation with regularity in the parameter space. (They) characterize the transition to chaos and the stabilization of the dynamics by revealing the nonlinearity of the parameters (squareness, ellipticity, and hardness) via the computation of Poincaré surfaces of section and the Lyapunov exponent across the parameter space. (They) expect (Their) work to introduce a valuable tool to increase understanding of the onset of chaos in soft billiards. >>

A. González Andrade, H. N. Núñez-Yépez, M. A. Bastarrachea-Magnani. Chaos and regularity in an anisotropic soft squircle billiard. Phys. Rev. E 112, 064213. Dec 22, 2025.

https://journals.aps.org/pre/abstract/10.1103/4xhm-r64f

arXiv: 2504.20270v2 [nlin.CD]. 28 Apr 2025

https://arxiv.org/abs/2504.20270

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

Keywords: gst, chaos, billiard, hard-wall billiards, soft billiards, particles, transitions.

# brain: meditative absorption shifts brain dynamics toward criticality.

<< ️Criticality describes a regime between order and chaos that supports flexible yet stable information processing. Here (AA) examine whether neural dynamics can be volitionally shifted toward criticality through the self-regulation of attention. >>

<< (They) examined ten experienced practitioners of meditation during a 10-day retreat, comparing refined states of meditative absorption, called the jhanas, to regular mindfulness of breathing. (They) collected electroencephalography (EEG) and physiological data during these practices and quantified the signal's dynamical properties using Lempel-Ziv complexity, signal entropy, chaoticity and long-range temporal correlations. In addition, (They) estimated perturbational sensitivity using a global auditory oddball mismatch negativity (MMN) during meditation. >>

<< ️Relative to mindfulness, jhana was associated with pronounced self-reported sensory fading, slower respiration, higher neural signal diversity across multiple measures, reduced chaoticity, and enhanced MMN amplitude over frontocentral sites. Spectral analyses showed a flatter aperiodic one over f component and a frequency-specific reorganization of long-range temporal correlations. Together, increased diversity with reduced chaoticity and heightened deviance detection indicate a shift toward a metastable, near-critical regime during jhana. >>

<< ️(AA) propose an overlap of the phenomenology of jhana with minimal phenomenal experiences in terms of progressive attenuation of sensory content with preserved tonic alertness. Accordingly, (Their) findings suggest that criticality is a candidate neurophysiological marker of the absorptive, minimal-content dimension of the minimal phenomenal experience. >>

Jonas Mago, Joshua Brahinsky, Mark Miller, et al. Meditative absorption shifts brain dynamics toward criticality. arXiv: 2511.20990v1 [q-bio.NC]. Nov 26, 2025.

https://arxiv.org/abs/2511.20990

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

Keywords: gst, brain, Zen, criticality, transitions, meditation, meditative absorption, jhanas, breathing mindfulness.

# 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.