Noise Normalization and Front Propagation in a Convective Bistable Model: Independent Mathematical Observations on Ramirez-Moya and Clerc (2026)

This technical note presents independent mathematical observations concerning the article by L. B. Ramirez-Moya and M. G. Clerc, Noise-sustained flashing structures in bistable systems, published in Chaos, Solitons & Fractals 213 (2026), Article 119345. The analysis focuses on the following mathematical and numerical aspects: Stochastic noise normalization: We examine the numerical description of uniformly and Gaussian-distributed random variables and identify a variance discrepancy unless an additional transformation or rescaling is applied. Kramers escape-time approximation: We clarify the factor-of-two convention arising in a scalar stochastic differential equation with diffusion amplitude (\sqrt{\zeta}), while distinguishing this calculation from the unresolved activation problem for the full spatial stochastic model. Exact traveling-front velocities: We derive explicit traveling-wave solutions for the deterministic cubic reaction–diffusion–advection equation and discuss the velocity sign conventions used in Figure 1 of the original article. Boundary conditions and numerical verification: We independently calculate the bistable equilibria, check the reported left boundary condition, and provide numerical benchmarks for deterministic front propagation and stochastic first-passage times. Reproducibility: We identify implementation details that would benefit from clarification, including random-number generation, stochastic increment scaling, front detection, and the effective velocity used in emission-size predictions. The note distinguishes exact mathematical identities from conditional theoretical arguments and numerical illustrations. The accompanying simulations are independent benchmarks and do not reproduce the experimental measurements or Figures 3–4 of the original article. Scope and conclusion: The findings identify specific mathematical and methodological questions deserving further clarification. They do not establish that the experimentally observed noise-sustained flashing structures are invalid, nor do they claim a demonstrated fatal error in the published work. AI-assistance disclosure and author responsibility: OpenAI ChatGPT assisted with English-language editing, algebraic consistency checks, draft preparation, and auxiliary numerical verification. The named author is responsible for independently checking all mathematical claims and accepts full responsibility for the construction of any counterexamples, lemmas, theorems, and proofs. Original article: https://doi.org/10.1016/j.chaos.2026.119345