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Record W2057221583 · doi:10.1142/s021812740100233x

DEGENERATE BIFURCATION ANALYSIS ON A PARAMETRICALLY AND EXTERNALLY EXCITED MECHANICAL SYSTEM

2001· article· en· W2057221583 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueInternational Journal of Bifurcation and Chaos · 2001
Typearticle
Languageen
FieldMathematics
TopicAdvanced Differential Equations and Dynamical Systems
Canadian institutionsWestern University
FundersNatural Sciences and Engineering Research Council of CanadaNational Natural Science Foundation of China
KeywordsHomoclinic orbitDegenerate energy levelsBifurcationHeteroclinic bifurcationEigenvalues and eigenvectorsHomoclinic bifurcationExcited stateAmplitudeMathematicsClassical mechanicsCodimensionMathematical analysisMechanical systemZero (linguistics)Heteroclinic cycleSymmetry (geometry)Bifurcation theoryPhysicsNonlinear systemGeometryQuantum mechanics

Abstract

fetched live from OpenAlex

A general parametrically and externally excited mechanical system is considered. The main attention is focused on the dynamical properties of local bifurcations as well as global bifurcations including homoclinic and heteroclinic bifurcations. In particular, degenerate bifurcations of codimension 3 are studied in detail. The original mechanical system is first transformed to averaged equations using the method of multiple scales. With the aid of normal form theory, the explicit expressions of the normal form associated with a double-zero eigenvalue and Z 2 -symmetry for the averaged equations are obtained. Based on the normal form, it has been shown that a parametrically and externally excited mechanical system can exhibit homoclinic and heteroclinic bifurcations, multiple limit cycles, and jumping phenomena in amplitude modulated oscillations. Numerical simulations are also given to verify the good analytical predictions.

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.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.748
Threshold uncertainty score0.445

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

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.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.031
GPT teacher head0.327
Teacher spread0.296 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it