Bibliographic record
Abstract
In the previous chapter generic features of spiral wave dynamics in oscillatory media were described on the basis of the complex Ginzburg–Landau equation. Spiral waves can also exist in complex oscillatory media where the local dynamics can have period-doubled or even chaotic oscillations. In regimes where complexoscillatory behavior is found, the new feature that appears in spiral waves is a line defect across which the phase of the oscillation changes by 2pi;. The presence of line defects leads to spatiotemporal patterns not seen in media with simple local oscillatory dynamics. Complex periodic or chaotic oscillations do not have simple single-loop trajectories in concentration phase space. For example, a period- n limit cycle is described by a period- n orbit that loops n times in concentration phase space before closing on itself (see Fig. 27.1). In such circumstances no simple single-valued angle variable may be introduced to play the role of the phase. It is often possible to generalize the definition of phase, even for systems whose dynamics is chaotic, and this is related to the phenomenon of phase synchronization (Rosenblum et al ., 1997; Pikovsky et al ., 2001; Osipov et al ., 2003). A spiral wave is an example of a self-organized structure that is a result of phase synchronization in a medium with complex local dynamics. Reaction–diffusion equation studies (Goryachev and Kapral, 1996a, 1996b; Goryachev et al ., 1998, 2000) and experiments (Yoneyama et al ., 1995; Park and Lee, 1999, 2002; Guo et al ., 2004; Park et al ., 2004) have demonstrated that spiral waves with synchronization defect lines exist in spatially distributed systems that undergo period-doubling bifurcations.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| 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 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.013 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".