A class of fractional-order discrete map with multi-stability and its digital circuit realization
Bibliographic record
Abstract
Abstract In this paper, a class of nonlinear functions and Gaussian function are modulated to construct a new high-dimensional discrete map. Based on Caputo fractional-order difference definition, the fractional form of the map is given, and its dynamical behaviors are explored. The three discrete maps with different nonlinear functions are compared and analyzed by bifurcation diagrams and Lyapunov exponents, especially the dynamical phenomena that evolve with the order. In addition, the maps have multiple rich stability, including homogeneous and heterogeneous coexistence attractors and hyperchaos coexistence attractors. The spectral entropy (SE) algorithm is used to measure the complexity of one-dimensional and two-dimensional maps. Performance tests show that the fractional-order map has more complex dynamics than the original map. Finally, the new maps were successfully implemented on the digital platform, which shows the simplicity and feasibility of the map implementation. The experimental results provide a reference for the research on the multi-stability of fractional discrete maps.
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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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".