Quantify fidelity of delay-oscillator emulation of complex network dynamics

Determine the quantitative accuracy with which the dynamics of coupled bistable delayed-feedback oscillators with long time delay and diffusive inter-oscillator coupling reproduce the collective behavior observed in complex networks of coupled oscillators, particularly multiplex networks with inter-layer coupling between replica nodes, across phenomena such as wavefront propagation and stochastic resonance.

Background

The paper investigates whether and how coupled bistable delayed-feedback oscillators can emulate the dynamics of multilayer (multiplex) networks, where inter-layer coupling links replica nodes. Using numerical simulations and electronic experiments, the authors demonstrate qualitative reproduction of multiplexing impacts on wavefront propagation and stochastic resonance, including control via coupling strength and noise.

Despite these demonstrations, the authors explicitly note uncertainty regarding how accurately the delay-oscillator dynamics replicates the collective behavior of complex oscillator networks. They further caution that delay systems may exhibit additional effects (e.g., delay-induced multistability and chaos), underscoring the need for a rigorous quantitative assessment of emulation fidelity for applications such as reservoir computing and Ising-machine-based optimization.