Stochastic binary networks with asymmetric and time-delayed interactions

2026-07-16

AI Summary

Traditional theories of stochastic binary networks struggle to capture the dynamics of systems featuring both asymmetric couplings and propagation delays. This work addresses this gap by combining analytical derivations with multi-spin numerical simulations to investigate stochastic binary networks incorporating time delays and asymmetric interactions. The study reveals, for the first time, that time delays can drive the stationary probability distribution toward uniformity while simultaneously preserving strong oscillatory temporal correlations. This coexistence is explicitly demonstrated in a five-spin model, and it is further shown that an external bias field can restore interaction-determined non-uniform stationary states. These findings suggest that asymmetry and time delay may serve as functional resources in neuromorphic hardware implementations.

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.

Problem

• stochastic binary networks
• asymmetric interactions
• time-delayed interactions
• non-equilibrium dynamics
• neuromorphic computation

Innovation

• stochastic binary networks
• time-delayed interactions
• asymmetric couplings
• neuromorphic computation
• temporal correlations