2106.06100
DYNAMICS OF A GENERALIZED RAYLEIGH SYSTEM
Maíra Duran Baldissera, Jaume Llibre, Regilene Oliveira
wronghigh confidenceCounterexample detected
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
Both sources prove existence and uniqueness of a limit cycle for the generalized Rayleigh system. However, the paper states the stability classification with the sign reversed (stable if a < 0, unstable if a > 0), whereas the candidate correctly concludes stable if a > 0 and unstable if a < 0. The paper’s own proof route uses a time-reversal to apply a Liénard uniqueness/stability theorem and then invokes a topological equivalence that again includes time reversal; this conflates orientation and flips stability. A direct Liénard reduction without reversing time, together with the energy identity Ḣ = a y^2(1 − y^{2n}), shows the unique limit cycle is attracting when a > 0 and repelling when a < 0. Hence the model’s classification is correct and the paper’s is sign-flipped. See the paper’s Theorem 1 and its proof, including the time-reversal steps and the quoted Liénard theorem .
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The manuscript assembles standard but valuable tools (Poincaré compactification, Liénard uniqueness) to give a global picture of the generalized Rayleigh system and correctly establishes existence and uniqueness of the limit cycle. However, the main theorem’s stability classification is stated with the wrong sign, apparently due to time-reversal steps used to apply a Liénard theorem and to pass between signs of a. This is central to the result and must be corrected and clarified.