Wavefront propagation in a bistable dual-delayed-feedback oscillator: analogy to networks with nonlocal interactions

TL;DR

This paper demonstrates that a bistable oscillator with dual delayed feedback can emulate network behaviors with nonlocal interactions, affecting wavefront propagation and stability, validated through simulations and experiments.

Contribution

It introduces a novel bistable oscillator model with two delays that replicates nonlocal network interactions, revealing new control mechanisms for wavefront dynamics.

Findings

Dual delays speed up wavefront propagation.

Adding a second delay stabilizes fronts at lower noise levels.

Experimental results confirm numerical simulations.

Abstract

In the present research, a bistable delayed-feedback oscillator with two delayed-feedback loops is shown to replicate a network of bistable nodes with nonlocal coupling. It is demonstrated that certain aspects of the nonlocal interaction impact on wavefront propagation identified in networks of bistable elements are entirely reproduced in the dynamics of a single oscillator with two delays. In particular, adding the second delayed-feedback loop allows speeding up both deterministic and stochastic wavefront propagation, achieving stabilization of propagating fronts at lower noise intensity and preventing fronts from noise-induced destruction occurring in the presence of single delayed-feedback. All the revealed effects are studied in numerical simulations and confirmed in physical experiments, showing an excellent correspondence.