# gst: synchronization and chaos in complex systems with delayed interactions.

<< Explaining the wide range of dynamics observed in ecological communities is challenging due to the large number of species involved, the complex network of interactions among them, and the influence of multiple environmental variables. >>

AA << consider a general framework to model the dynamics of species-rich communities under the effects of external environmental factors, showing that it naturally leads to delayed interactions between species, and analyze the impact of such memory effects on population dynamics. >>

<< Employing the generalized Lotka-Volterra equations with time delays and random interactions, (AA) characterize the resulting dynamical phases in terms of the statistical properties of community interactions. (Their) findings reveal that memory effects can generate persistent and synchronized oscillations in species abundances in sufficiently competitive communities. This provides an additional explanation for synchronization in large communities, complementing known mechanisms such as predator-prey cycles and environmental periodic variability. >>

<< Furthermore, (AA) show that when reciprocal interactions are negatively correlated, time delays alone can induce chaotic behavior. This suggests that ecological complexity is not a prerequisite for unpredictable population dynamics, as intrinsic memory effects are sufficient to generate long-term fluctuations in species abundances. >>

Francesco Ferraro, Christian Grilletta, et al. Synchronization and chaos in complex ecological communities with delayed interactions. arXiv: 2503.21551v1 [q-bio.PE]. Mar 27, 2025.

https://arxiv.org/abs/2503.21551

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

Keywords: gst, pause, silence, random, chaos, chaotic behavior, network, delay, time delay, delayed interactions, random interactions, memory effect 

# gst: even tight-binding billiards could exhibit chaotic behaviors

<< Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common property of all quantum-chaotic quadratic Hamiltonians studied in this context so far is the presence of random terms that act as a source of disorder. >>

AA << introduce tight-binding billiards in two dimensions, which are described by non-interacting spinless fermions on a disorder-free square lattice subject to curved open boundaries. >>

They <<  show that many properties of tight-binding billiards match those of quantum-chaotic quadratic Hamiltonians (..) these properties indeed appear to be consistent with the emergence of quantum chaos in tight-binding billiards. This statement nevertheless needs to be taken with some care since there exist a sub-extensive (in lattice volume) set of single-particle eigenstates that are degenerate in the middle of the spectrum at zero energy (i.e., zero modes), for which the agreement with RMT (random matrix theory) predictions may not be established. >>

Iris Ulcakar, Lev Vidmar. Tight-binding billiards. arXiv:2206.07078v1 [cond-mat.stat-mech]. Jun 14, 2022. 

https://arxiv.org/abs/2206.07078

Also

keyword 'billiard' in FonT

https://flashontrack.blogspot.com/search?q=billiard

keyword 'chaos' | 'chaotic' in Font

https://flashontrack.blogspot.com/search?q=chaos

https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=caos

https://inkpi.blogspot.com/search?q=caotico

keywords: gst, billiard, chaos, chaotic behavior