# 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: 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: evolving fractal dimensions in iterative bicolored percolation.

<< ️Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. (AA)  introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and transform fractal dimensions. >>

<< ️Starting from critical configurations, such as the O⁡(𝑛) loop and fuzzy Potts models, successive coarse graining generates a hierarchy of distinct yet critical generations. Using the conformal loop ensemble, (They) derive exact, generation-dependent fractal dimensions, which are quantitatively confirmed by large-scale Monte Carlo simulations. The evolutionary trajectory depends not only on the universality class of the initial state but also on whether it possesses a two-state critical structure, leading to different critical exponents starting from site and bond percolation. >>

<< ️These results establish a general geometric mechanism for evolving fractal dimensions, in which scale invariance persists across generations. >>

Shuo Wei, Haoyu Liu, Xin Sun, et al. Evolving fractal dimensions in iterative bicolored percolation. Phys. Rev. E 113, L032102. Mar 23, 2026.

https://journals.aps.org/pre/abstract/10.1103/s2ql-zxz6#4eafda38-c97e-4656-8034-9a3682fa0218

arXiv: 2511.18462v2 [cond-mat.stat-mech]. Mar 24, 2026. 

https://arxiv.org/abs/2511.18462

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

Keywords: gst, order, disorder, fluctuations, percolation, fractal dimensions, criticality, coarse-graining transformations.

# 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: comparative analysis of detonation and shock waves interacting with droplets.

<< ️The interaction mechanisms among detonation waves, shock waves, and liquid droplets play a critical role in advancing propulsion technologies such as rotating detonation engines. This (AA) study conducts a detailed comparison of wave dynamics, cavitation phenomena, and droplet deformation during the detonation wave and the shock-wave interactions with a water droplet, employing a high-resolution numerical model that integrates multicomponent compressible fluid dynamics, chemical reactions, and phase transition effects. >>

<< ️Numerical simulations reveal distinct characteristics between detonation and shock-induced phenomena. Unlike the shock wave, detonation-induced reflected shock waves exhibit significantly higher propagation velocities while maintaining nearly identical wave configurations, a phenomenon this (AA) study mechanistically explains by the unique postwave conditions. >> 

<< ️A fundamental distinction arises in cavitation dynamics between the detonation wave and the shock wave, with the detonation-wave triggering cavitation zone collapse at significantly higher rates compared with the shock wave. This difference is attributed to the shorter persistence of low-pressure regions behind the detonation front, where rapid attenuation of postwave pressure and flow velocity occurs. >>

<< ️Moreover, detonation-induced flow interactions create unique droplet fragmentation patterns. The rapid postwave velocity reduction prevents Rayleigh-Taylor instability-driven forward jet formation, instead causing leeward-side flattening of the droplet through the vortex in the recirculation zone. >>

Hanbing Zou, Xin Jin, Haotian Chen, et al. Comparative analysis of detonation  and shock waves interacting with droplets: Characteristics and mechanisms. Phys. Rev. Fluids 11, 034303. Mar 18, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/mp9z-tlk3  

Also: waves, drop, droplet, droploid, bubble, collapse, vortex, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, shock-waves, drop, droplet, droploid, bubble, collapse, vortex, transitions, phase transition, cavitation, detonation wave, detonation front, droplet fragmentation patterns. 

# gst: to tune to a damage, the damage spreading transition.

<< ️Deterministic classical cellular automata can be in two phases, depending on how irreversible the dynamical rules are. In the strongly irreversible phase, trajectories with different initial conditions coalesce quickly, while in the weakly irreversible phase, trajectories with different initial conditions can remain different for a time exponential in the system volume. The transition between these phases is referred to as the damage-spreading transition (the "damaged" sites are those that differ between the trajectories). >>

<< ️(AA) develop a theory for this transition. In the simplest and most generic setting, the transition is known to be related to directed percolation, one of the best-studied nonequilibrium phase transitions. However, (They) show that full theory of the damage-spreading critical point is richer than directed percolation, and contains an infinite hierarchy of sectors of local observables. >>

<< ️Directed percolation describes the first level of the hierarchy. The higher observables include "overlaps" for multiple trajectories, and may be labeled by set partitions. (These higher observables arise naturally if, for example, we consider decay of entropy under the irreversible dynamics.). The full hierarchy yields a hierarchy of nonequilibrium fixed points for reaction-diffusion-type processes, all of which contain directed percolation as a subsector, but which possess additional universal critical exponents. >>

Adam Nahum, Sthitadhi Roy. The damage spreading transition: a hierarchy of renormalization group fixed points. arXiv: 2603.22439v1 [cond-mat.stat-mech]. Mar 23, 2026.

https://arxiv.org/abs/2603.22439

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

Keywords: gst, transitions, damage, damage-spreading transition, directed percolation. 

# gst: early warning signals for primary and secondary bifurcation to oscillatory instabilities.

<< ️In several natural and engineering systems, changes in control parameters can trigger bifurcations that lead to sustained or growing periodic oscillations, indicating the onset of oscillatory instabilities. Such emergent behaviour often results from positive feedback between interacting subsystems, resulting in large-amplitude oscillations that can be detrimental. >>

<< ️Several precursors are available to provide early warning of an impending oscillatory instability. In reality, practical systems may exhibit different sequences of bifurcations, including a primary bifurcation to an oscillatory state that may be either continuous or abrupt, followed by an abrupt secondary bifurcation, and further transitions beyond the secondary bifurcation. Existing precursors for oscillatory instabilities typically forewarn the onset of the primary bifurcation to an oscillatory state and tend to saturate once the system enters the oscillatory regime. Notably, primary bifurcations often involve lower amplitudes compared to the more severe states after secondary bifurcation. >>

<< ️In this study, (AA) propose a methodology based on spectral visibility graphs to get forewarning for both primary and secondary bifurcations. The method inherently captures the evolution of the harmonic content of the signal relative to other frequency components. The approach employs tuning of a single sensitivity parameter to detect different sequences of bifurcation. (They) demonstrate the usefulness of (Their) method for thermo-acoustic and aero-acoustic instabilities in multiple engineering systems involving turbulent flow and reactions. (Their) methodology can help systems prepare in advance or even avoid undesirable transitions. Tuning the sensitivity parameter allows adaptive, risk-based warnings, ensuring high performance without tipping into undesirable regimes. >>

Rohit Radhakrishnan, Prasana Kumar, Induja Pavithran, et al. Early warning signals for primary and secondary bifurcation to oscillatory instabilities. arXiv: 2603.24068v1 [physics.flu-dyn]. Mar 25, 2026.

https://arxiv.org/abs/2603.24068

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

Keywords: gst, instability, turbulence, transitions, bifurcation, feedback.

# gst: apropos of different degrees of decimation, reduction of triadic interactions suppresses intermittency and anomalous dissipation in turbulence.

<< ️(AA) investigate how the defining statistical features of three-dimensional turbulence respond to systematic reductions of the Fourier-space triadic interaction network. Using direct numerical simulations of both fractally and homogeneously decimated Navier-Stokes dynamics, (They) show that progressive thinning of the set of active modes leads to a systematic suppression of intermittency and, most strikingly, to the vanishing of the mean dissipation rate in the large-Reynolds-number limit. >>

<< ️Structure-function exponents collapse onto their dimensional values, the multifractal singularity spectrum contracts, and the analyticity width extracted from the exponential spectral tail increases monotonically with decimation-each indicating a substantial regularization of the velocity field. >>

<< ️Together, these results provide direct evidence that anomalous dissipation in incompressible turbulence is not a generic property of the Navier-Stokes equations, but instead requires the full combinatorial richness of their triadic nonlinear interactions. >>

Anikat Kankaria, Ritwik Mukherjee, Sugan Durai Murugan, et al. Reduction of triadic interactions suppresses intermittency and anomalous dissipation in turbulence. arXiv: 2603.19180v1 [physics.flu-dyn]. Mar 19, 2026.

https://arxiv.org/abs/2603.19180

Also: turbulence, intermittency, dissipation, singularity, collapse, transition, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, turbulence, three-dimensional turbulence, incompressible turbulence, intermittency, dissipation, anomalous dissipation, singularity, multifractal singularity spectrum contracts, collapse, transitions, networks, triadic interactions, progressive thinning, decimation.

# gst: apropos of flows of hyperpycnal river plumes

<< ️The flow of a hyperpycnal river plume into a lake with a sloping bed and without any lateral confinement is a common occurrence in nature. A characteristic example of such geophysical fluid flow system is the inflow of river Rhone in Llake Geneva. >>

<< ️In this work, (AA) study the near-field plunging dynamics of an unconfined hyperpycnal plume at laboratory scale, over an idealized bed, with a slope that is similar to the one of the natural system. The study is based on large-eddy simulation of the Navier-Stokes equations in the Boussinesq approximation. (They) focus on the effect of varying the inflow conditions and in particular the densimetric Froude number, Fr_𝑑, which is the nondimensional parameter describing the ratio between inertial and buoyancy forces acting on the plume. >>

<< ️Three simulations were performed at different values of Fr_𝑑, within the range encountered in the natural system. Similarly to previous works, (They) are able to identify lateral slumping as the main mechanism that leads to plunging of the dense river water and the formation of the characteristic triangular pattern at the lake surface. (They) are able to further identify the formation of a wake downstream of the vertex plunge point, due to the transport of mixed river-ambient water from the converging mixing layers across the plunge curve on both sides of the plume. >>

<< ️The extent of both the wake and the overall plunge region increases significantly with increase of Fr_𝑑. This mechanism can be associated to the changes of the surface patterns of the plume observed in the field. In addition, (AA) compute the total entrainment, 𝐸, of ambient lake water as the streamwise increase of volumetric flow rate downstream of the river mouth. 𝐸 is found to increase with distance from the mouth, as the plume continuously entrains ambient lake water. >> 

<< (They) find that for the same distance from the river mouth, 𝐸 is larger for lower Fr_𝑑. This increase of 𝐸 with decreasing Fr_𝑑 is attributed to two mechanisms. First, in the plunge region, lower Fr_𝑑 leads to greater lateral spread and therefore increased interface area between plume and ambient water. Second, in the underflow region, lower Fr_𝑑 results in higher mean streamwise plume velocity, enhancing entrainment intensity. >>

Georgios Giamagas, Cyrille Bonamy, Koen Blanckaert, et al. Plunging and entrainment dynamics of an unconfined hyperpycnal plume over a sloping bed. Phys. Rev. Fluids 11, 033801. Mar 5, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/41p1-sn3p

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

Keywords: gst, vortex, vortices, transitions, unconfined hyperpycnal plume, lateral confinements, near-field plunging dynamics, inertial and buoyancy forces, lateral slumping, wake downstream of the vertex plunge point, lateral spread, streamwise plume velocity.

# brain: entraining chimeras, the effect of driving with regular, irregular, and real-world phases.

<< ️Chimera states in coupled oscillator networks are paradigmatic examples of partial synchronization in nonlinear systems, with direct relevance to real-world network dynamics, such as neuronal dynamics. Since real-world networks are not isolated, but embedded in larger interacting systems, chimeras have also been studied under the influence of other networks and external signals. In particular, most prior work has treated periodic forcing of chimeras in the thermodynamic limit. >>

<< ️As a consequence, it remains unclear how chimera states respond to external driving in finite-size networks, where they can spontaneously collapse into full synchronization. It is also largely unknown how realistic noisy drivers, rather than periodic signals, affect driver-response synchronization. >>

<< ️To address these open questions, (AA) drive a finite-size oscillator network that exhibits a chimera state with constant-angular-frequency phases and with the same phases superimposed with noise. (They) find that, for a specific range of angular-frequency mismatch and driving strength, (They) can entrain chimeras without causing them to collapse into full synchronization. Adding noise, in turn, reduces entrainment and facilitates collapses. >>

<< ️As a real-world application of the driven chimera state framework, (AA) also drive chimeras with phases from focal and nonfocal electroencephalography (EEG) signals recorded during seizure-free periods in patients with epilepsy. (They) observe that focal signals yield higher entrainment power, within-network coherence, and collapse power than nonfocal signals when the driver EEG's dominant frequency is close to the chimera's mean angular frequency. Away from this regime, nonfocal signals yield higher values of all three measures. The observed differences not only characterize focal and nonfocal signals, but may also provide additional insight into the seizure-free brain dynamics of epilepsy patients. >>

<< ️In conclusion, beyond quantifying how external driving signals, with or without noise, affect the dynamics of chimera states that can collapse into full synchronization, this (AA) work further bridges the study of chimera states and epilepsy research. >>

Jacopo Epifanio, Martin Brešar, Ralph G. Andrzejak. Entraining chimeras: The effect of driving with regular, irregular, and real-world phases. Phys. Rev. E 113, 034214. Mar 13, 2026.

https://journals.aps.org/pre/abstract/10.1103/vczh-r59d

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

Keywords: gst, brain, chimeras, noise, transitions, collapse, networks, coupled oscillator networks, epilepsy, synchronization, driver-response synchronization. 

# gst: redirecting counter-moving swarms through collision.

<< ️Multi-swarm systems, where two or more swarms of mobile agents occupy the same region of space with different parameters and goals, occur in a variety of biological, engineering, and defense applications. Composites of multiple swarms can produce hybrid spatiotemporal patterns, which compared to single swarming systems, are relatively unexplored. >>

<< ️In this work, (AA) develop a framework for studying the collision of counter-moving swarms, each with its own preferred, stable velocity before collision. (They) show that redirection of such swarms after collision occurs when a stable velocity synchronized state of the multi-swarm composite exists. Using a rigid-body approximation, (They) are able to extract how scatter-redirection transitions scale with swarm parameters in a variety of scenarios from reciprocal and non-reciprocal systems to symmetric and antagonistic parameter values. (They) results compare well to simulations of both particle modeled agents and wheeled robots. >>

Jason Hindes, Chinthan B. Prasad, Loy McGuire, et al. Redirecting counter-moving swarms through collision. arXiv: 2603.12002v1 [nlin.AO]. Mar 12, 2026.

https://arxiv.org/abs/2603.12002

Also: swarm, swarmalators, particle, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, swarms, particles, transitions, scatter-redirection transitions, multi-swarm systems, collisions, collision of counter-moving swarms.

# 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: from fluttering to drifting: inertialess sedimentation of an achiral particle.

<< ️There has been much recent interest in the chiral motion of achiral particles that sediment in a viscous fluid in a regime where inertial effects can be neglected. This occurs in a broad range of applications such as those involving biological objects like algae, ultrathin graphene flakes, or colloidal suspensions. It is known that particles with two planes of symmetry can be categorized as “settlers,” “drifters,” or “flutterers,” where the latter sediment along chiral trajectories despite their achiral shapes. >>

<< ️Previous work investigated the sedimentation of circular disks bent into a U-shape and identified them as “flutterers.” In this work (AA) analyze the change in behavior of such particles when (They) break one of their symmetries by pinching the disks isometrically along their axis, a shape change that can arise during the sedimentation of thin elastic sheets. The “fluttering” behavior is found to be robust to such shape changes, with the trajectories now evolving toward helical paths. However, the behavior changes when the degree of pinching becomes too strong, at which point the particles become “drifters” which sediment steadily without rotation. >>

<< ️(AA) establish criteria for the transition between the two types of behavior and confirm (Their) predictions in experiments. Finally, (AA) discuss the implications of (Their) observations for the dispersion of dilute suspensions made of such particles. >>

Christian Vaquero-Stainer, Tymoteusz Miara, Anne Juel, et al. From fluttering to drifting: Inertialess sedimentation of an achiral particle. Phys. Rev. Fluids 11, 034102. March 10, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/scj8-6lpf

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

Keywords: gst, behaviors, particles, achiral particles, settlers, drifters, flutterers.

# 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.

# brain: collective dynamics in spiking neural networks beyond Dale's principle.

<< ️Dale's Principle has historically guided neuroscience research as a valuable rule of thumb, namely that all synapses on each neuron release the same set of neurotransmitters. Most existing Spiking Neuron Network models share this dichotomous assumption that neurons are either excitatory or inhibitory; however, recent experimental evidence points towards co-release mechanisms that violate this assumption. >>

<< ️Here, (AA) introduce a minimal model of "Bilingual" neurons violating Dale's principle that can exert both excitatory and inhibitory effects. (They) identify parameter regimes in which this architecture exhibits transitions between synchronous and asynchronous dynamics that differ quantitatively from those observed in a matched monolingual control architecture. >>

<< ️(AA) report distinct information-processing signatures both at the level of neurons and higher-order interactions between them near the phase transitions. These (AA) results suggest that the population of neurons violating Dale's principle may provide an alternative mechanism for regulating large-scale oscillatory activity in neural circuits. >>

Ross Ah-Weng, Hardik Rajpal. Collective Dynamics in Spiking Neural Networks Beyond Dale's Principle. arXiv: 2602.23202v1 [q-bio.NC]. Feb 26, 2026.

https://arxiv.org/abs/2602.23202

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

Keywords: gst, brain, neuro, networks, transitions, neural circuits, spiking neuron networks, excitatory and inhibitory effects, Dale's principle, Henry Hallett Dale, bilingual neurons, transitions between synchronous and asynchronous dynamics.

# gst: multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials.

<< ️(AA) address the existence, stability, and dynamics of single-ring and multi-ring vorticity-carrying necklace solitons under the action of the Kerr nonlinearity and a Bessel-lattice potential modulated in the azimuthal direction. The model may be realized in the spatial domain for bulk optical waveguides, the spatiotemporal domain for optical cavities, and for effectively two-dimensional Bose-Einstein condensates. The setup supports single- and multi-ring necklace vortex patterns, including monopoles, dipoles, tripoles, quadrupoles, pentapoles, sextupoles, octupoles, and 12-poles. >>

<< ️In contrast with the inherent instability of conventional vortex beams with high topological charges (winding numbers), vortex necklace-shaped solitons with large winding numbers are found to be stable in the present setup. In particular, octupoles exhibit stable breathing dynamics, and 12-pole necklaces with high winding numbers may be stable. >>

<< ️These (AA) findings provide a new way for generating stable vortex necklaces, offering a vast potential for manipulations of complex spatiotemporal light fields. >>

Ruolan Zhao, Jing Chen, Boris A. Malomed, et al. Multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials. arXiv: 2602.18703v1 [physics.optics]. Feb 21, 2026.

https://arxiv.org/abs/2602.18703

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

Keywords: gst, vortex, solitons, vortex necklace-shaped solitons, single-ring vorticity, multi-ring vorticity, stable vortex necklace, transitions.

# 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: spatiotemporal noise stabilizes unbounded diversity in strongly-competitive communities.

<< ️Classical ecological models predict that large, diverse communities should be unstable, presenting a central challenge to explaining the stable biodiversity seen in nature. (AA) revisit this long-standing problem by extending the generalized Lotka-Volterra model to include both spatial structure and environmental fluctuations across space and time.  >>

<< ️(They) find that neither space nor environmental noise alone can resolve the tension between diversity and stability, but that their combined effects permit arbitrarily many species to stably coexist despite strongly disordered competitive interactions. (They) analytically characterize the noise-induced transition to coexistence, showing that spatiotemporal noise drives an anomalous scaling of abundance fluctuations, known empirically as Taylor's law. >>

<< ️At the community level, this manifests as an effective sublinear self-inhibition that renders the community stable and asymptotically neutral in the high-diversity limit. Spatiotemporal noise thus provides a novel resolution to the diversity-stability paradox and a generic mechanism by which complex communities can persist. >>

Amer Al-Hiyasat, Daniel W. Swartz, Jeff Gore, et al. Spatiotemporal noise stabilizes unbounded diversity in strongly-competitive communities. arXiv: 2602.13423v1 [q-bio.PE]. Feb 13, 2026.

https://arxiv.org/abs/2602.13423

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

Keywords: gst, noise, spatiotemporal noise, disorder, transition, noise-induced transition, disordered competitive interactions, spatial structure and environmental fluctuations.

# gst: phase-controlled elastic, inelastic, and coalescent collisions of two-dimensional flat-top solitons.

<< ️(AA) investigate elastic, inelastic, and coalescent collisions between two-dimensional flat-top solitons supported by the cubic-quintic nonlinear Schrödinger equation. Numerical simulations reveal distinct collision regimes ranging from nearly elastic scattering to strongly inelastic interactions leading to long-lived merged states. >>

<< ️(They) demonstrate that the transition between these regimes is primarily controlled by the relative phase of the solitons at the collision point, with out-of-phase collisions suppressing overlap and in-phase collisions promoting strong interaction. >>

<< ️Kinetic-energy diagnostics are introduced to quantitatively characterize collision outcomes and to identify phase- and separation-dependent windows of elasticity. To interpret the observed dynamics, (They) extract effective phase-dependent interaction potentials from collision trajectories, providing a mechanical picture of attraction and repulsion between flat-top solitons. The stability of merged states formed after strongly inelastic collisions is explained by their lower energetic cost, arising from interfacial energetics, where a balance between internal pressure and edge tension plays a central role. A variational analysis based on direct energy minimization supports this picture by revealing robust energetic minima associated with stationary two-dimensional flat-top solitons. >>

M. O. D. Alotaibi, Y. O. A. Abughnheim, L. Al Sakkaf, et al. Phase-controlled elastic, inelastic, and coalescent collisions of two-dimensional flat-top solitons. arXiv: 2602.07762v1 [nlin.PS]. Feb 8, 2026.

https://arxiv.org/abs/2602.07762

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

Keywords: gst, soliton, transitions, elastic, inelastic, and coalescent collisions, elastic scattering interactions, strongly inelastic interactions, long-lived merged states, attraction, repulsion, internal pressure, edge tension.