# gst: near the Hopf boundary, Intermittency and chimera states.

AA << study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. >>️

<< For analysis, (AA) first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors. Consequently, different oscillators may show a dynamics that is intermittently synchronized (or desynchronized), giving rise to intermittent chimera states. The behavior of the intermittent laminar phases is characterized by the characteristic time spent in the synchronization manifold, which decays as a power law. >>

<< Such intermittent dynamics is quite general and is also observed in an ensemble of a large number of oscillators arranged in variety of network topologies including nonlocal, scale-free, random, and small-world networks. >>️

Anjuman Ara Khatun, Yusra Ahmed Muthanna, et al. Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states. Phys. Rev. E 109, 034208. March 15, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.034208

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

Keywords: gst, transition, intermittency, chaos, chimera, network

# gst: soft and stiff modes in colloidal particle networks

<< Floppy microscale spring networks are widely studied in theory and simulations, but no well-controlled experimental system currently exists. >> 

AA << show that square lattices consisting of colloid-supported lipid bilayers functionalized with DNA linkers act as microscale floppy spring networks. (AA) extract their normal modes by inverting the particle displacement correlation matrix, showing the emergence of a spectrum of soft modes with low effective stiffness in addition to stiff modes that derive from linker interactions. >>

<< Evaluation of the softest mode, a uniform shear mode, reveals that shear stiffness decreases with lattice size. >>

 AA << results reveal the importance of entropic steric effects. >>

️

Julio Melio, Silke E. Henkes, Daniela J. Kraft. Soft and Stiff Normal Modes in Floppy Colloidal Square Lattices. Phys. Rev. Lett. 132, 078202. Feb 14, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.078202

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

Keywords: gst, particle, nano, colloids, network, colloidal network

# gst: self-repelling species could self-organize.

<< Catalytically active particles form clusters when they respond not only to their own chemical targets but to those of other catalysts, too. >>️

AA  << show that the phenomenon of self-organization depends strongly on the network topology. >>️

They << modeled a three-species system (..) systems where each species responds chemotactically only to its own substrate cannot self-organize unless one species is self-attracting. >>️

<< Next, they developed a model that allowed species to respond to both their substrates and their products. Pair interactions between different species in this more complex model drove an instability that spread throughout the three-species system, causing the catalysts to clump together. Surprisingly, this self-organization process occurred even among particles that were individually self-repelling. >>️

Rachel Berkowitz. Self-Repelling Species Still Self-Organize. Physics 16, s128. Sept 19, 2023. 

https://physics.aps.org/articles/v16/s128

Vincent Ouazan-Reboul, Ramin Golestanian, Jaime Agudo-Canalejo. Network effects lead to self-organization in metabolic cycles of self-repelling catalysts. Phys. Rev. Lett. 131, 128301. Sep 19, 2023. 

http://dx.doi.org/10.1103/PhysRevLett.131.128301

Also: self-assembly, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, self-assembly, network,  topology.

# gst: emergence of chimeras driven by non-normality

<< The emergence of order in nature manifests in different phenomena, with synchronization being one of the most representative examples. >>️

<< Particular attention has been paid to the emergence of chimera states, where subsets of synchronized oscillations coexist with asynchronous ones. Such coexistence of coherence and incoherence is a perfect example where order and disorder can persist in a long-lasting regime. >>

<< Based on a symmetry-breaking mechanism, in this paper, (AA) shed light on the role that non-normality, a ubiquitous structural property of real networks, has in the emergence of several diverse dynamical phenomena, e.g., amplitude chimeras or oscillon patterns. >>️

<< Specifically, (they) demonstrate that the prevalence of source or leader nodes in networks leads to the manifestation of phase chimera states. >>️

Riccardo Muolo, Joseph D. O'Brien, et al. Persistence of chimera states and the challenge for synchronization in real-world networks. arXiv: 2306.00237v1 [nlin.PS]. May 31, 2023.

https://arxiv.org/abs/2306.00237

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

Keywords: gst, chimera, network, synchronization, swarm, noise, order, disorder, normal

# gst: chimera resonance, in analogy with the effects of stochastic and coherence resonance

AA << explore numerically the impact of additive Gaussian noise on the spatio-temporal dynamics of ring networks of nonlocally coupled chaotic maps. >>

️

<<  It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. >>

<< This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance. >>️

Elena Rybalova, Vasilii Nechaev, Eckehard Schöll, Galina Strelkova. Chimera resonance in networks of chaotic maps. arXiv:2307.00006v2 [cond-mat.dis-nn]. Jul 5, 2023.

https://arxiv.org/abs/2307.00006

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

Keywords: gst, chimera, noise, chaos, network, chimera resonance

# gst: sudden phase transitions among nonconservative system with nonreciprocal interactions

<< A nonconservative system with nonreciprocal interaction has been found to reveal exotic features where sudden phase transitions can occur. >>️

Here AA reported << the emanation of a chimera in a network of Stuart-Landau oscillators. >>

<< The findings could have pragmatic implications in the areas of active matter, networks, and photonics. >>

️

M. Paul Asir. Emergence of chimeras: An impetus by exceptional points. Phys. Rev. E 108, 024220. Aug 22, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.024220

Also: Stuart–Landau equation. 

https://en.m.wikipedia.org/wiki/Stuart%E2%80%93Landau_equation

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

Keywords: network, transition, chimera, chaos, pattern formation

# gst: neural networks know their knots.

<< The use of neural networks in physics is booming. Recently, the tool has helped researchers uncover everything from new magnetic materials (..) to ways to reduce noise in electron beams produced at synchrotrons (..) Seeking their own neural network success, (AA) wondered if the tool could classify knots, a computationally challenging problem. >>

They << applied two different neural networks to the problem—a recurrent neural network (RNN) and a feed-forward neural network (FFNN). >>

<< The RNN achieved 99% accuracy >>

 

Katherine Wright. Neural Networks Know Their Knots. Physics 13, s19. Feb 11, 2020.

https://physics.aps.org/articles/v13/s19.

img  https://physics.aps.org/assets/b3a39285-5bde-4137-8a54-5f9d9b9e2738/es19_1.png

Olafs Vandans, Kaiyuan Yang, et al. Identifying knot types of polymer conformations by machine learning. Phys. Rev. E 101, 022502. Feb 11, 2020.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.022502

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

Keywords: gst, network, neural network, knots

# gst: emergence of the traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera in a two-dimensional network

<< Neuronal synchronization being a phenomenon linked to several brain pathologies such as epilepsy, Parkinson diseases, Alzheimer, autism and schizophrenia, does not always appear in a singular way in neuronal networks. Its presence (state of coherence) accompanied simultaneously by an asynchronous state (state of incoherence) has been demonstrated (..) in the networks of identical oscillators not locally coupled. This phenomenon was later termed the chimera state. (..) Chimera states are analogously to the cerebral behaviors of certain aquatic mammals and migratory birds, which during their movements half part of their brains asleep while the rest are awake.  >>️

AA << study the emergence of the traveling chimera state in a two-dimensional network of (..) burst neurons with the mutual presence of local and non-local couplings. (AA) show that in the unique presence of the non-local chemical coupling modeled by a nonlinear function, the traveling chimera phenomenon occurs with a displacement in both directions of the plane of the grid. The introduction of local electrical coupling shows that the mutual influence of the two types of coupling can, for certain values, generate traveling chimera, imperfect-traveling, traveling multi-clusters, and alternating traveling chimera, ie the presence in the network under study, of patterns of coherent elements interspersed by other incoherent elements in movement and alternately changing their position over time. The confirmation of the states of coherence is done by introducing the parameter of instantaneous local order parameter in two dimensions. >>️

Gael R. Simo, Patrick Louodop, et al. Traveling chimera patterns in two-dimensional neuronal network. arXiv:2106.08400v1. Jun 9, 2021.

https://arxiv.org/abs/2106.08400