Desynchronization and pattern formation in a noisy feedforward oscillators network

TL;DR

This paper investigates how small additive noise in a directed array of coupled oscillators can lead to desynchronization and complex pattern formation, driven by non-normal couplings that amplify perturbations beyond linear stability predictions.

Contribution

It reveals the role of non-normal directed couplings in amplifying noise-induced perturbations, leading to novel desynchronization and pattern formation in oscillator networks.

Findings

Noise causes desynchronization in the array.

Non-normal couplings amplify perturbations.

System evolves to a non-trivial attractor before destabilization.

Abstract

We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is studied in a region of the parameters that would yield deterministic synchronization. Non normal directed couplings seed a coherent amplification of the perturbation: this latter manifests as a modulation, transversal to the limit cycle, which gains in potency node after node. If the lattice extends long enough, the initial synchrony gets eventually lost and the system moves toward a non trivial attractor, which can be analytically characterized as an asymptotic splay state. The noise assisted instability, ultimately vehiculated and amplified by the non normal nature of the imposed couplings, eventually destabilizes also this second attractor. This phenomenon yields spatiotemporal patterns, which cannot be anticipated by a conventional linear stability analysis.