MULTI-PULSE HETEROCLINIC ORBITS AND CHAOTIC MOTIONS IN A PARAMETRICALLY EXCITED VISCOELASTIC MOVING BELT
Bibliographic record
Abstract
This paper investigates the multi-pulse global heteroclinic bifurcations and chaotic dynamics for nonlinear, nonplanar oscillations of the parametrically excited viscoelastic moving belts by using an extended Melnikov method in the resonant case. Applying the method of multiple scales, the Galerkin's approach and the theory of normal form, the explicit normal form is obtained for the case of 1:1 internal resonance and primary parametric resonance. Studies are performed for the heteroclinic bifurcations of the unperturbed system and for the characteristics of the hyperbolic dynamics of the dissipative system, respectively. The extended Melnikov method is used to investigate the Shilnikov type multi-pulse bifurcations and chaotic dynamics of the viscoelastic moving belt. Based on the investigation, the geometric structure of the multi-pulse orbits is described in the four-dimensional phase space. Numerical simulations show that the Shilnikov type multi-pulse chaotic motions can occur. Furthermore, numerical simulations lead to the discovery of the new shapes of chaotic motion. Overall, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists.
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.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
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 | 0.001 | 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)
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".