# 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: 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: chimera states in wheel networks

<< ️How higher-order interactions influence dynamical behavior in networks of coupled chaotic oscillators remains an open question. To address this, (AA) investigate emergent dynamical behaviors in a wheel network of Rössler and Lorenz oscillators that incorporates both pairwise (1-simplex) and higher-order (2-simplex) interactions under three coupling schemes, namely, diffusive, conjugate, and mean-field diffusive coupling. >>

<< ️(AA) numerical analysis reveals four distinct collective behaviors: synchronization, desynchronization, chimera states, and synchronized clusters. To systematically classify these dynamical behaviors, (They) introduce two statistical measures that effectively capture synchronization patterns among arbitrarily positioned nodes. Applying these measures across all dynamical models and coupling schemes (six different models in total), (They) show that both pairwise and higher-order interactions crucially influence the emergence and robustness of chimera states. (They) observe that under pairwise interaction alone, chimera states appear with high prevalence in specific coupling ranges, though the robustness depends on both the coupling scheme and the underlying dynamical system. >>

<< Incorporation of higher-order interactions reveals that the higher-order interaction underlying diffusive coupling enhances chimera states in both Rössler and Lorenz networks; under conjugate coupling, it strengthens chimera states in Lorenz but instead promotes full synchronization in Rössler; and under mean-field diffusive coupling, higher-order interactions generally favor synchronization, particularly for Rössler oscillators, but promote chimera in the Lorenz system for the intermediate range of its strengths. >>

<< ️Overall, (AA) results demonstrate that higher-order interactions can significantly modulate, promote, or suppress chimera states depending on the coupling mechanism and oscillator dynamics. >>

Ashwathi Poolamanna, Medha Bhindwar, Chandrakala Meena. Chimera States in Wheel Networks. arXiv: 2601.01411v1 [nlin.CD]. Jan 4, 2026.

https://arxiv.org/abs/2601.01411

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

Keywords: gst, chimera, network, transitions

# 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: intermittent motility of a synthetic active particle in changing environments.

<< ️(AA) experimentally investigate the dynamics of synthetic active particles composed of gravitationally bouncing, superwalking droplets confined within an annular fluid bath. >>

<< ️Driven by a topologically pumping dual-frequency waveform, the droplets exhibit alternating active (walking) and dormant (bouncing) phases, producing intermittent azimuthal motion. Tracking individual droplets reveals pseudolaminar chaotic dynamics in the time series of particle's angular position, characterized by laminar plateaus that are interrupted by short irregular bursts of activity. >>

<< ️Increasing the driving amplitude induces a qualitative change in the active particle's intermittent dynamics, arising from a symmetry-breaking transition in its Faraday-wave field environment: continuous SO(2)-symmetric "channelling" waves give way to discrete "trapping" patterns. >>

<< ️These findings demonstrate how environmental symmetry and spatiotemporal structure modulate motility and intermittency in synthetic active matter. >>

Rudra Sekhri, Rahil N. Valani, Tapio Simula. Intermittent Motility of a Synthetic Active Particle in Changing Environments. arXiv: 2512.16135v1 [physics.flu-dyn]. Dec 18, 2025.

https://arxiv.org/abs/2512.16135 

Also: drop, droplet, droploid, intermittency, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, active matter, drops, droplets, droploids, intermittency, behavior, active walking phase, dormant bouncing phase,  trapping patterns.

# 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: 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: 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

# 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: 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: 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.