2408.08140
Dynamical behaviors of the special fractional-order Chen-Lee system
Mihai Ivan
wronghigh confidenceCounterexample detected
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 4 correctly derives the Jacobian spectrum at e_m^2 and applies Matignon’s test in most cases, but item 2(ii) is wrong: it asserts instability for ac<0 on the real interval (−√(3ac), √(3ac)), which is empty over ℝ and conceptually misclassifies the ac<0, Δ>0 regime; with ac<0 one has det B>0 for all m, so λ± share the sign of tr B=a−c, giving stability when a<c and instability when a>c, independent of m within Δ>0. This flaw is visible in the theorem statement and proof sketch in the PDF, and the model’s solution provides the correct classification and threshold q2 for the complex-eigenvalue case via Matignon’s criterion , using the standard stability test for Caputo systems .
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The article delivers a concrete and mostly correct stability classification for a special fractional Chen–Lee system with control by leveraging standard linearization and Matignon’s criterion. However, the theorem’s case 2(ii) is incorrect both algebraically and conceptually, and it misclassifies the ac<0, Δ>0 regime. Fixing this error and clarifying boundary cases would render the work suitable for publication aimed at specialists.