# 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 

# brain: time delay in 'reservoir brain' as a reservoir network, a hypothesis

<< Both the predictive power and the memory storage capability of an artificial neural network called a reservoir computer increase when time delays are added into how the network processes signals, according to a new model. >>️

<< They also suggest that incorporating time delays could offer advantages to living neural networks (such as those found in human and animal brains). Such a finding would be tantalizing, as time delays are known to decrease performance in living systems. For example, for a baseball player facing an oncoming ball, a longer time delay between perception and action (which is learned from experience) will decrease the likelihood they hit a home run. Are there instead cases in which time delays increase an organism’s ability to perform some task? Has evolution shaped our brains, which could perhaps be thought of as a collection of reservoir computers, so that the time delay between one neuron sending a signal and a second receiving it is exactly the right length for understanding the visual and audio that constantly impinge upon our eyes and ears? Does adding time delays impact the number of neurons the brain needs to operate correctly? Further work is needed to answer these questions, but such work could lead to a new understanding of how biological organism’s function.  >>️

Sarah Marzen. Time Delays Improve Performance of Certain Neural Networks. Physics 17, 111. July 22, 2024. 

https://physics.aps.org/articles/v17/111 

Also: pause, silence, jazz, network, brain, ai (artificial intell), in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, network, neural network, reservoir network, reservoir computer, time delay, ai, artificial intelligence