Noise-induced nonreciprocal topological dissipative solitons in directionally coupled chains and lattices

TL;DR

This paper investigates noise-sustained topological dissipative solitons in nonreciprocally coupled chains, revealing their properties, bifurcations, and critical behavior through analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of noise-induced topological solitons in nonreciprocal systems, combining bifurcation theory and numerical validation.

Findings

Bifurcation analysis of steady states in nonreciprocal systems.

Identification of noise-sustained topological phase wall dynamics.

Critical points where soliton size diverges with specific power laws.

Abstract

Nonreciprocal coupling can alter the transport properties of material media, producing striking phenomena such as unidirectional amplification of waves, boundary modes, or self-assembled pattern formation. It is responsible for nonlinear convective instabilities in nonlinear systems that drive topological dissipative solitons in a single direction, producing a lossless information transmission. Considering fluctuations, which are intrinsic to every macroscopic dynamical system, noise-sustained structures emerge permanently in time. Here, we study arrays of nonreciprocally coupled bistable systems exhibiting noise-sustained topological phase wall (or soliton) dynamics. The bifurcations between different steady states are analytically addressed, and the properties of the noise-sustained states are unveiled as a function of the reciprocal and nonreciprocal coupling parameters. Furthermore, we study critical points where the structures' characteristic size diverges with different power law exponents. Our numerical results agree with the theoretical findings.