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arxiv: 2411.15065 · v1 · submitted 2024-11-22 · 🌊 nlin.PS · nlin.AO· physics.app-ph

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

David Pinto-Ramos , Karin Alfaro-Bittner , Ren\'e G. Rojas , Marcel G. Clerc This is my paper

Pith reviewed 2026-05-23 17:37 UTC · model grok-4.3

classification 🌊 nlin.PS nlin.AOphysics.app-ph
keywords nonreciprocal couplingtopological solitonsnoise-sustained structuresbistable systemsdissipative solitonsdirectionally coupled chainspower-law divergencephase walls
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The pith

Nonreciprocal coupling in bistable arrays produces noise-sustained topological solitons that propagate unidirectionally and grow in size with power-law divergences at critical points.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines how directionally coupled chains and lattices of bistable systems can host noise-induced topological phase walls, also called dissipative solitons. The authors show that nonreciprocal coupling enables these structures to persist due to fluctuations and move in one direction. They analytically describe the bifurcations separating different steady states and how the solitons' size and other properties change with the strengths of reciprocal and nonreciprocal couplings. At certain critical coupling values, the characteristic size of these structures diverges following power laws with distinct exponents. Numerical simulations confirm the theoretical predictions for these behaviors.

Core claim

In arrays of nonreciprocally coupled bistable systems, noise sustains topological phase walls that exhibit unidirectional dynamics, with bifurcations between steady states determined analytically as a function of the coupling parameters, and the structures' size diverging according to power laws with different exponents at critical points.

What carries the argument

The noise-sustained topological phase wall, or dissipative soliton, in directionally coupled bistable chains and lattices, which enables the unidirectional propagation and persistence under fluctuations.

If this is right

  • Analytical expressions for bifurcations between steady states as functions of reciprocal and nonreciprocal coupling.
  • Properties of noise-sustained states vary with the coupling parameters.
  • Characteristic size of the structures diverges with different power law exponents at critical points.
  • Numerical results match the theoretical findings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This mechanism suggests a way to achieve robust, unidirectional information transfer in noisy environments using simple coupled systems.
  • The power-law behavior at critical points indicates universal scaling properties that could be tested in various physical realizations of bistable units.
  • Generalization to lattices implies potential for controlling patterns in two-dimensional nonreciprocal media.

Load-bearing premise

The model assumes linear directional coupling between bistable units that can be tuned independently while preserving bistability of each unit.

What would settle it

An experiment or simulation showing that the soliton size does not follow the predicted power-law divergences when approaching the critical coupling values would falsify the central claim.

Figures

Figures reproduced from arXiv: 2411.15065 by David Pinto-Ramos, Karin Alfaro-Bittner, Marcel G. Clerc, Ren\'e G. Rojas.

Figure 1
Figure 1. Figure 1: Discrete systems with nonreciprocal coupling. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Dynamics of the nonreciprocally coupled Frenkel-Kontorova lattice. a) Case [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Phase diagram of Eq. (2) for planar solutions [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of noise in the dynamical regions of the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Behavior of the characteristic length of the sys [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: System of two pendula for values of the nonre [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript studies arrays of bistable units with independent linear reciprocal and nonreciprocal directional coupling, showing that additive noise sustains unidirectional topological phase walls (dissipative solitons). Bifurcations between steady states are treated analytically, the characteristic soliton size is shown to diverge with distinct power-law exponents at critical points depending on the coupling parameters, and direct numerical integration is reported to agree with the theory.

Significance. If the derivations hold, the work provides an analytical handle on noise-sustained unidirectional solitons in nonreciprocal lattices and identifies parameter-dependent critical scaling, which is of interest for dissipative pattern formation and directed transport in nonlinear media.

major comments (2)
  1. [Model equations and bifurcation analysis] The entire bifurcation structure and the reported power-law exponents for soliton size are derived under the assumption of purely linear directional coupling (reciprocal plus nonreciprocal terms) while each unit remains bistable. No robustness check against even weak nonlinear coupling perturbations is presented; such terms would generically alter the fixed-point landscape and the scaling exponents.
  2. [Analytical treatment and numerical comparison] The abstract asserts that bifurcations are analytically addressed and that numerics agree with theory, yet the provided text supplies neither the explicit steady-state equations, the linearization steps, nor any error or truncation analysis that would allow verification of the claimed power laws.
minor comments (1)
  1. [Abstract] Notation for the reciprocal and nonreciprocal coupling strengths should be introduced once and used consistently; the abstract refers to them only descriptively.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Model equations and bifurcation analysis] The entire bifurcation structure and the reported power-law exponents for soliton size are derived under the assumption of purely linear directional coupling (reciprocal plus nonreciprocal terms) while each unit remains bistable. No robustness check against even weak nonlinear coupling perturbations is presented; such terms would generically alter the fixed-point landscape and the scaling exponents.

    Authors: We acknowledge that the derivations rely on the assumption of linear directional coupling, which enables the analytical treatment of bifurcations and the power-law scaling of soliton size. Nonlinear coupling terms would indeed generically modify the fixed-point structure and exponents. The manuscript presents the linear case as a foundational model for noise-sustained unidirectional solitons. In revision we will add a brief discussion of this modeling assumption and its limitations, noting that robustness to weak nonlinear perturbations remains an open question for future study. This is a partial revision. revision: partial

  2. Referee: [Analytical treatment and numerical comparison] The abstract asserts that bifurcations are analytically addressed and that numerics agree with theory, yet the provided text supplies neither the explicit steady-state equations, the linearization steps, nor any error or truncation analysis that would allow verification of the claimed power laws.

    Authors: To improve clarity and verifiability, we will revise the manuscript by adding an appendix that explicitly presents the steady-state equations, the linearization procedure around the relevant fixed points, and a short discussion of numerical agreement including any truncation or discretization considerations used in the simulations. This will directly address the request for details that allow independent verification of the reported power-law exponents. revision: yes

Circularity Check

0 steps flagged

No circularity: analytical bifurcations derived directly from model equations

full rationale

The paper states a model of arrays of bistable units with independent linear reciprocal and nonreciprocal coupling, then analytically addresses steady-state bifurcations and power-law divergences of soliton size at critical points as functions of those parameters. Numerical integration is used only for verification and agreement with the derived expressions. No step reduces a prediction to a fitted input by construction, invokes a self-citation as the sole justification for a uniqueness claim, or renames an empirical pattern; the derivation chain remains self-contained against the stated equations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The abstract provides no explicit list of free parameters or invented entities; the model is described only at the level of 'arrays of nonreciprocally coupled bistable systems' whose coupling strengths are varied. Standard assumptions of white noise and ordinary differential equations for each unit are implicit but not detailed.

axioms (1)
  • domain assumption The system is governed by a set of coupled ordinary differential equations with bistable local potentials and linear directional coupling terms.
    Required for the analytical bifurcation analysis mentioned in the abstract.

pith-pipeline@v0.9.0 · 5701 in / 1284 out tokens · 32702 ms · 2026-05-23T17:37:53.840302+00:00 · methodology

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