AI summaryⓘ
The authors studied networks where tiny units switch on and off randomly but interact in ways that aren't balanced and have delays in their communication. They found that these delays cause the network to show strong back-and-forth activity, similar to what experiments have seen, even when the overall state seems evenly spread out. Interestingly, these uniform states still have meaningful time patterns, unlike what you'd expect from just random noise at high temperatures. Their math and computer tests show these effects happen in small and slightly bigger networks. This work helps understand how timing and imbalance in connections shape complex behaviors, useful for brain-inspired computing and network science.
stochastic binary networksasymmetric interactionstime delaysuperparamagnetic tunnel junctionsoscillatory temporal correlationssteady-state probabilitysymmetry-breakingneuromorphic computingcomplex networksspin systems
Authors
Hantao Zhang, Sidra Gibeault, Matthew W. Daniels, Philippe Talatchian, Ursula Ebels, Advait Madhavan, Mark D. Stiles
Abstract
Stochastic binary networks are widely used to describe collective dynamics in complex systems and to perform neuromorphic computation, yet realistic networks often contain both asymmetric interactions and finite signal propagation times that fall outside conventional theories. Here we study stochastic binary networks with asymmetric and time-delayed interactions motivated by experimental observations in coupled superparamagnetic tunnel junctions. We find that time delay fundamentally reshapes the dynamics induced by anti-symmetric couplings, producing strong oscillatory temporal correlations consistent with experiment. At the same time, sufficiently long delays drive the steady-state probabilities toward equal state occupations even in strongly coupled systems. These apparently featureless probability distributions coexist with pronounced temporal correlations, distinguishing them from equilibrium high-temperature behavior. We further show analytically that delay-induced uniform distributions emerge in a broad class of stochastic networks, while symmetry-breaking bias fields restore interaction-dependent steady states with qualitatively modified behavior. Simulations of networks with five coupled spins demonstrate that these effects persist beyond minimal systems with only two spins. Our results establish a unified framework for stochastic binary networks in the intermediate regime between symmetric instantaneous interactions and asymmetric or time-delayed interactions, and suggest that asymmetry and delay can be exploited as functional resources in neuromorphic hardware and complex network dynamics.