HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS
Why is this work in the frame?
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Full frame distilled prediction
Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
- Candidate categories
- none
- Consensus categories
- none
- Domain
- Candidate signal: noneConsensus signal: none
- Study design
- Candidate signal: Theoretical or conceptualConsensus signal: Theoretical or conceptual
- Genre
- Candidate signal: EmpiricalConsensus signal: none
- Teacher disagreement score
- 0.817
- Threshold uncertainty score
- 0.335
- Validation status
machine_predicted_unvalidated·codex-gemma-dda1882f352a
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
- Teacher spread
- 0.326 · how far apart the two teachers sit on this one work
- Validation status
score_only:v0-immature-baseline· verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it
Abstract
In this paper, we consider bifurcation of limit cycles in near-Hamiltonian systems. A new method is developed to study the analytical property of the Melnikov function near the origin for such systems. Based on the new method, a computationally efficient algorithm is established to systematically compute the coefficients of Melnikov function. Moreover, we consider the case that the Hamiltonian function of the system depends on parameters, in addition to the coefficients involved in perturbations, which generates more limit cycles in the neighborhood of the origin. The results are applied to a quadratic system with cubic perturbations to show that the system can have five limit cycles in the vicinity of the origin.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
The record
- Venue
- International Journal of Bifurcation and Chaos
- Topic
- Advanced Differential Equations and Dynamical Systems
- Field
- Mathematics
- Canadian institutions
- Western University
- Funders
- not available
- Keywords
- Hamiltonian systemMathematicsQuadratic equationBifurcationLimit cycleLimit (mathematics)Hamiltonian (control theory)Mathematical analysisHopf bifurcationApplied mathematicsControl theory (sociology)PhysicsMathematical optimizationComputer scienceNonlinear systemGeometryQuantum mechanics
- Has abstract in OpenAlex
- yes