Bifurcation analysis of bursting solutions of two Hindmarsh-Rose neurons with joint electrical and synaptic coupling
Bibliographic record
Abstract
In this paper, we investigate the dynamic behavior of a system oftwo coupled Hindmarsh-Rose (HR) neurons, based on bifurcationanalysis of its fast subsystem. The individual HR neuron has chaoticbehavior, but they can become regularized when coupled throughsynaptic coupling or joint electrical-synaptic coupling. Throughnumerical methods we first investigate the bifurcation structure of its fastsubsystem. We show that the emerging of periodic patterns ofneurons is related to topological changes of its underlyingbifurcations. The Lyaponov exponent calculations further reveal thepathway from chaotic bursting behavior to regular bursting of HRneurons. Finally, we include both electrical and synaptic couplingin the system, and numerically calculate the time dynamics. Eventhough electrical couplings (or gap junctions) usually does notregularize chaotic trajectories, but joint coupling has been moreeffective than synaptic coupling alone in producing stable rhythms.The main contribution of this paper is that we provide amathematical description for transitions of neuron dynamics fromchaotic trajectories to regular bursting when synaptic andelectrical-synaptic coupling strengthens, using bifurcationanalysis.
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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 | 0.001 |
| 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 | 0.000 |
| 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".