# brain: minimal network of brain dynamics; hierarchy of approximations to quasicritical neural network dynamics.

<< ️(AA) present an interacting model of neural network dynamics that incorporates key biological features, including multiple forms of inhibitory interactions. (They) develop a hierarchy of analytical mean-field approximations to characterize nonequilibrium phase transitions between ordered, disordered, and chaotic regimes, complemented by a detailed stability analysis. >> 

<< ️(AA) show that inhibition generically enhances the stability of network dynamics. The model is consistent with the quasicriticality hypothesis, exhibiting regions of maximal dynamical susceptibility and mutual information, modulated by the strength of external stimuli. (They) further demonstrate that, at the mean-field level, the critical transition belongs to the mean-field directed percolation universality class, in agreement with prior experimental and theoretical studies. More broadly, (Their) framework may offer insights into neurological disorders, with the unstable regime exhibiting chaotic dynamics that may be associated with epileptic seizures. >>

Jeremy B. Goetz, Naruepon Weerawongphrom, Rashid V. Williams-García, et al. Minimal network of brain dynamics: Hierarchy of approximations to quasicritical neural network dynamics. Phys. Rev. E 114, 044321. Oct 22, 2026.

https://journals.aps.org/pre/abstract/10.1103/64b7-qb8p

arXiv: 2512.22093v2 [cond-mat.dis-nn]. Jul 15, 2026.

https://arxiv.org/abs/2512.22093

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

Keywords: brain, neurons, networks, transitions, neuronal network activity, percolation phase transition, cortical networks, criticality.

# gst: apropos of decorrelation in turbulence, space-time correlations of passive scalars in colored-noise flows.

<< ️The space-time correlation of a passive scalar advected by a Gaussian colored-noise velocity with wavenumber-dependent correlation times and power-law spatial spectra (by AA) is investigated. Within the inertial-convective subrange, (They) derive an analytical solution for the space-time correlation. >>

<< ️(AA) results clarify the underlying decorrelation mechanism of passive scalars: mean-flow advection and large-scale sweeping dominate temporal decorrelation, and small-scale distortion dominates spatial decorrelation. >>

Long Wang, Guowei He. Space-time correlations of passive scalars in colored-noise flows. arXiv: 2604.07052v2 [physics.flu-dyn]. Oct 2, 2026.

https://arxiv.org/abs/2604.07052

Phys. Rev. E 114, 045106. Oct 22, 2026.

https://journals.aps.org/pre/abstract/10.1103/z1s1-kspl

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

Keywords: gst, turbulence, transitions, noise, space-time correlation, inertial-convective subrange, random-sweeping mechanism, mean-flow advection, large-scale sweeping, small-scale distortion. 

# brain: dynamics of random recurrent neural networks; colored noise and sublinear activations.

<< ️(AA) study the dynamics of recurrent neural networks with random couplings, sublinear odd activation functions, and temporally correlated noise. Using large N methods, (They) determine stationary correlations and distinguish the loss of local linear stability from the onset of chaos, characterized by a positive largest Lyapunov exponent. >>

<< These thresholds delimit an intermediate regime in which local instability coexists with asymptotic stability under a common noise history. Their separation depends on both the noise correlation time and the asymptotic growth of the activation function. (AA) show that internal noise with any finite correlation time cuts off the divergence of the network’s intrinsic correlation time τ_(corr) at the edge of chaos; it exhibits a critical scaling τ_(corr,max) ∼ 1/√D_0, where D_0 is the integrated noise strength. >>

<< Static random input instead produces coincident thresholds and a divergent correlation time. (AA) also calculate the frequency-dependent participation dimension from a four-point correlation function. Its zero-frequency value is inversely proportional to the fourth power of the network correlation time, predicting a smooth minimum at the weak-noise chaos threshold. Numerical simulations support the large-network predictions and reveal appreciable finite-size effects. >>

German Mato, Facundo Rigatuso, Gonzalo Torroba. Dynamics of random recurrent neural networks: colored noise and sublinear activations.  arXiv: 2610.31575v1 [q-bio.NC]. Oct 22, 2026.

https://arxiv.org/abs/2610.31575

Also: brain, network, chaos, soliton, disorder, noise, in https://www.inkgmr.net/kwrds.html 

Keywords: brain, network, chaos, solitons, disorder, noise, weak-disorder expansion, white and colored noise, quenched noise.

# gst: kinetics and stability of transition waves in viscoelastic bistable lattices.

<< ️Transition waves are central to phase-boundary propagation in solid phase transformations and sequential state switching in multistable metamaterials. However, existing studies are often limited to specific structural prototypes or simplified constitutive models, failing to reveal how wave kinetics and stability can be independently modulated by bistable element parameters. >>

<< ️Here, (AA) investigate transition waves in viscoelastic bistable lattices using a trilinear constitutive model with independently tunable parameters. (..) Results indicate that the energy release rate, boundary strain, transition zone width, and wave profile are strongly regulated by damping and the stiffness characteristics of the bistable spring. Floquet analysis supports the proposed macroscopic criterion that instability arises when the energy release rate decreases with increasing wave velocity, and further reveals that the stable velocity region is mainly governed by the stiffnesses of both the untransformed and transformed phases. >>

<< ️Time-domain simulations show that low-velocity waves are typically unstable, manifesting in two distinct postinstability behaviors: they either split into two separated linear waves and a pinned transition interface, or self-adjust toward a more stable propagation state. >>

<< ️Finally, a Riemann-type initial value problem is considered to determine the initial strain conditions required to initiate transition waves at prescribed velocities. >>

<< ️These results establish a direct link between bistable constitutive parameters, kinetic relations, stability boundaries, postinstability evolution, and initiation conditions, providing a theoretical basis for designing transition-wave-mediated multistable metamaterials. >>

P.Q. Li, C. Wu, K.F. Wang, et al. Kinetics and stability of transition waves in viscoelastic bistable lattices. Phys. Rev. E 114, 044217. Oct 20, 2026.

https://journals.aps.org/pre/abstract/10.1103/rzgj-kq1h

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

Keywords: gst, waves, traveling-waves, wave chaos, transition waves, stability, instability, multistable metamaterials, viscoelastic bistable lattices.

# gst: emergence and coexistence of periodic and unstructured motion in future-avoiding random walks.

<< ️Self-avoiding random walks on graphs can be seen as walkers interacting with their own past history. Here, (AA) consider a complementary class of dynamics, mutual future-avoiding random walks (MFARWs), where stochastically driven walkers are avoiding each other's planned future trajectories. ️Such systems arise naturally in conceptual models of shared mobility. >>

<< ️(AA) show that periodic behavior emerges spontaneously in two different MFARWs, and that periodic and unstructured behavior coexist, providing an example of chimera like behavior of nonoscillatory paths on networks. >>

<< Further, (AA) analytically describe and predict the onset of structure. (They) find that the transition from unstructured to periodic behavior is driven by a mechanism of self-amplifying coupling to the periodic components of the stochastic drivers of the system. In the context of shared mobility applications, these states imply a regime of naturally stable coexistence between flexible and line-based public transport. >>

A. Schmaus, K. Stiller, N. Molkenthin. Emergence and coexistence of periodic and unstructured motion in future-avoiding random walks. Phys. Rev. E 114, 044219. Oct 23, 2026.

https://journals.aps.org/pre/abstract/10.1103/9q1j-dlw8

arXiv: 2602.03308v1 [nlin.AO]. Feb 3, 2026.

https://arxiv.org/abs/2602.03308

Also: walk, walking, random, behav, chimera, network, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, walk, walking, randomness, behavior, chimera, networks, transitions, mutual future-avoiding random walks (MFARWs), stochastically driven walkers, periodic behavior, self-amplifying coupling, discontinuous phase transition. 

# gst: wave-crests around obstacles in odd viscous liquids.

<< ️The values of liquid odd-viscosity coefficients remain largely unknown, with only one experimental measurement reported to date [Nat. Phys. 15, 1188 (2019)]. In this work, inspired by the well-known consequences of dispersion surfaces in classical liquids from the work of Lighthill, (AA) theoretically determine the shapes of constant-phase wave crests formed around obstacles moving at constant velocity in two- and three-dimensional odd viscous liquids, which may or may not undergo rigid rotation. From this analysis, (AA) derive parametric relations that the odd-viscosity coefficients must satisfy, providing a framework for their experimental determination. >>

E. Kirkinis, A. Levchenko. Wave-crests around obstacles in odd viscous liquids. Phys. Rev. Fluids 11, 104101. Oct 14, 2026.

https://journals.aps.org/prfluids/abstract/10.1103/sm6p-qky2

arXiv: 2511.07751v1 [physics.flu-dyn]. Nov 11, 2025.

https://arxiv.org/abs/2511.07751

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

Keywords: gst, waves, viscosity, liquid odd-viscosity coefficient, dispersion surfaces, constant-phase wave crests, hydrodynamic waves, waves and free surface flows. 

# gst: how mobile oscillators reshape dynamical robustness in complex networks.

<< ️While the robustness of collective dynamics in static networks is well established, how agent mobility and network topology jointly shape dynamical robustness remains largely unexplored. >>

<< ️In this letter, (AA) investigate the robustness of mobile Stuart-Landau oscillators performing random walks on networks and interacting diffusively when co-located. In the rapid-mobility regime, (They) reduce the dynamics to a mean-field framework linking network degree statistics to an effective global coupling strength. >> 

<< ️(AA) show analytically that increased degree heterogeneity in the network enhances the effective coupling strength, and strictly lowers the critical threshold of functional degradation for amplitude death. Numerical simulations confirm the predicted heterogeneity-dependent ordering of the transition thresholds, showing an earlier collective collapse in scale-free networks than in random or regular networks. >> 

<< ️(Their) results establish mobility and network heterogeneity as key determinants of robustness in mobile oscillator populations, with implications for resilient biological and engineered collectives. >>

Sayantan Nag Chowdhury, Srilena Kundu. How Mobile Oscillators Reshape Dynamical Robustness in Complex Networks. arXiv: 2610.16608v1 [nlin.AO]. Oct 12, 2026.

https://arxiv.org/abs/2610.16608

Also: network, random, walks, collapse, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, randomness, walks, collapse, mobile oscillators, mobility, transition thresholds.