# gst: when a continuous attractor could survive seemingly destructive bifurcations

<< Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability in general--they are destroyed by most infinitesimal changes of the dynamical law that defines them. >>️

AA << build on the persistent manifold theory to explain the commonalities between bifurcations from and approximations of continuous attractors. Fast-slow decomposition analysis uncovers the persistent manifold that survives the seemingly destructive bifurcation. Moreover, recurrent neural networks trained on analog memory tasks display approximate continuous attractors with predicted slow manifold structures. >>️

<< continuous attractors are functionally robust and remain useful as a universal analogy for understanding analog memory. >>

Ábel Ságodi, Guillermo Martín-Sánchez, Piotr Sokół, Il Memming Park. Back to the Continuous Attractor. arXiv: 2408.00109v1 [q-bio.NC]. Jul 31, 2024. 

https://arxiv.org/abs/2408.00109

Also: attractor, analogy, brain, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, attractor, continuous attractor, analogy, brain

# gst: evolution of turbulence using a random jet array

AA << perform a series of laboratory experiments in which (They) alter the parameters of the randomized algorithm, along with the jet spacing and outlet velocity of the jets. (They) first determine the location where turbulence transitions to a fully developed state and show that it is a function of jet penetration length, ℒ𝒥, and effective jet spacing, 𝑆𝑒. (AA)  identify three distinct regions for the spatial decay of turbulence in RJA (Random Jet Array) facilities and notably, (They) find different decay rates, unlike previous studies that report only one spatial decay rate using similar facilities. These regions are shown to depend on the variations of input parameters yet independent of the strength of the mean flow. (AA) also find the strength of the mean flow does not affect the homogeneity, nor the production, transport, or advection terms of the turbulent kinetic energy budget equation. >>

Finally, AA << address a longstanding question toward estimating turbulence metrics with an RJA based on the input parameters. >>

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Arefe Ghazi Nezami, Blair Anne Johnson. Evolution of turbulence using a random jet array. Phys. Rev. Fluids 9, 074610. Jul 26, 2024.

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.074610

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

Keywords: gst, turbulence

# behav: swarms and hybrids, an approach to create and control collective motions (on demand)

AA << demonstrate that it is possible to generate coordinated structures in collective behavior at desired moments with intended global patterns by fine-tuning an inter-agent interaction rule. (Their) strategy employs deep neural networks, obeying the laws of dynamics, to find interaction rules that command desired collective structures. The decomposition of interaction rules into distancing and aligning forces, expressed by polynomial series, facilitates the training of neural networks to propose desired interaction models. Presented examples include altering the mean radius and size of clusters in vortical swarms, timing of transitions from random to ordered states, and continuously shifting between typical modes of collective motions. This strategy can even be leveraged to superimpose collective modes, resulting in hitherto unexplored but highly practical hybrid collective patterns, such as protective security formations. >>

Dongjo Kim, Jeongsu Lee, Ho-Young Kim. Navigating the swarm: Deep neural networks command emergent behaviours. arXiv: 2407.11330v1 [cs.NE]. Jul 16, 2024.️

https://arxiv.org/abs/2407.11330

Also: swarm, flock, behav, AI (artificial intell), in https://www.inkgmr.net/kwrds.html 

Keywords: behav, swarm, flock, AI, artificial intelligence 

# game: hypothesis of a geometric design of chaotic attractors, on demand

AA << propose a method using reservoir computing to generate chaos with a desired shape by providing a periodic orbit as a template, called a skeleton. (They) exploit a bifurcation of the reservoir to intentionally induce unsuccessful training of the skeleton, revealing inherent chaos. The emergence of this untrained attractor, resulting from the interaction between the skeleton and the reservoir's intrinsic dynamics, offers a novel semi-supervised framework for designing chaos. >>️

Tempei Kabayama, Yasuo Kuniyoshi, et al. Designing Chaotic Attractors: A Semi-supervised Approach. arXiv: 2407.09545v1 [cs.NE]. Jun 27, 2024.

https://arxiv.org/abs/2407.09545

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

Keywords: game, chaos, chaotic attractors

# gst: collapse of a toroidal bubble inducing shock waves

<< When bubbles collapse near a wall, they typically experience an asymmetric deformation. This collapse leads to the creation of a jet that strikes the bubble interface, causing the formation of a toroidal bubble and the subsequent release of a water-hammer shock. >>️

AA << findings demonstrate that shock waves emitted from the toroidal bubble consistently propagate toward the central axis of the torus, resulting in significant pressure shocks along the axis, similar to the water-hammer shock formed during the collapse of a spherical bubble. >>️

<< In contrast, weak pressure waves are generated in the transverse directions, leading to relatively weaker pressure peaks. Furthermore, the wall-pressure peak induced by the toroidal bubble is approximately three times higher than that induced by the spherical bubble. >>️

Cheng Liu, Xiaobin Yang, et al. Investigations on the shock wave induced by collapse of a toroidal bubble. Phys. Rev. E 110, 015103. Jul 16, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.015103

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

Keywords: gst, bubble, drop, waves, collapse

# gst: Resonancelike emergence of chaos in complex networks of damped-driven nonlinear systems.

AA << solve a critical outstanding problem in this multidisciplinary research field: the emergence and persistence of spatiotemporal chaos in complex networks of damped-driven nonlinear oscillators in the significant weak-coupling regime, while they exhibit regular behavior when uncoupled. >>

They << uncover and characterize the basic physical mechanisms concerning both heterogeneity-induced and impulse-induced emergence, enhancement, and suppression of chaos in starlike and scale-free networks of periodically driven, dissipative nonlinear oscillators. >>️

Ricardo Chacon, Pedro J. Martínez. Resonancelike emergence of chaos in complex networks of damped-driven nonlinear systems. Phys. Rev. E 110, 014209. Jul 19, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.014209

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

Keywords: gst, network, resonance, chaos

# gst: steady, whirling, planar beating, and writhing transitions for active filaments.

FIG. 2. Images showing the steady, whirling, planar beating, and writhing states for active filaments

<< Biofilament-motor protein complexes are ubiquitous in biology and drive the transport of cargo vital for many fundamental life processes at the cellular level. As they move, motor proteins exert compressive forces on the filaments to which they are attached. If the filament is clamped or tethered in some way, this force leads to buckling and a subsequent range of dynamics. >>️

<< The transition between whirling and beating has not yet been explored, and a characterization of the complex writhing behavior observed at higher forcing has not been performed. Furthermore, previous studies have focused on how the whirling, beating, or writhing vary with the follower force, leaving the dependence of the emergent state on the filament aspect ratio, a key parameter related to the balance of the viscous and elastic forces, largely unexplored. >>

AA << utilize techniques from computational dynamical systems to determine and characterize these bifurcations. (They) track emerging time-periodic branches and identify quasiperiodic states (..) investigate the effect of filament slenderness on the bifurcations and, in doing so, present a comprehensive overview of the dynamics which emerge in the follower force model. >>

️

Bethany Clarke, Yongyun Hwang, Eric E. Keaveny. Bifurcations and nonlinear dynamics of the follower force model for active filaments. Phys. Rev. Fluids 9, 073101. Jul 15, 2024. 

https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.9.073101

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

Keywords: gst, bifurcation, transition, active filaments, microtubules, steady, whirling, planar beating, writhing