Analysis on an Oscillator With Delayed Feedback Near Double Hopf Bifurcations
Bibliographic record
Abstract
Abstract This paper considers the effect of time delayed feedbacks in a nonlinear oscillator with external forcing. The particular attention is focused on the case where the corresponding linear system has two pairs of purely imaginary eigenvalues at a critical point, leading to double Hopf bifurcations. An analytical approach is used to find the explicit expressions for the critical values of the system parameters at which non-resonant or resonant Hopf bifurcations may occur. A fourth-order Ronge-Kutta numerical integration scheme is applied to obtain the dynamical solutions in the vicinity of the critical points. Both the cases with and without the external forcing are considered. It has been found the system exhibits very rich complex dynamics including periodic, quasi-periodic and chaotic motions. Moreover, a sensitivity analysis is carried out to show that chaotic motions are very sensitive to the time delay. This suggests that the time delay can be used: (1) to control bifurcations and chaos; and (2) to generate bifurcations and chaos.
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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 | 0.000 | 0.001 |
| 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) | 0.002 | 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".