Population Dynamics in Networks of Izhikevich Neurons with Global Delayed Coupling
Bibliographic record
Abstract
Abstract. We investigate the collective dynamics of a network of heterogeneous Izhikevich neurons with global constant-delay coupling using a mean-field approximation, valid in the thermodynamic limit. The introduction of a biologically motivated synaptic current expression and a spike frequency adaptation mechanism give rise to significantly different bifurcation structures. Our study emphasizes the impact of heterogeneity in the quenched current, adaptation intensity, and synaptic delay on the emergence of collective oscillations. The effects of heterogeneity and adaptation vary across different scenarios but essentially result from the balance of excitatory drives, including input currents that cause neurons to spike, adaptation currents that terminate spiking, and synaptic currents that predominantly favor spiking in excitatory networks but hinder it in inhibitory cases. Our perturbation and bifurcation analysis reveal interesting transitions in the behavior in both limits of extremely weak heterogeneity and coupling strength. Finally, our analysis indicates that synaptic delays exhibit little impact on the generation of collective oscillations in weakly coupled heterogeneous networks. This effect becomes more pronounced with increasing heterogeneity. Moreover, a larger delay does not necessarily enhance the likelihood of oscillations, especially in weakly adapting neural networks. Beyond that, delays primarily function as an excitatory drive, promoting the emergence of oscillations and even inducing new macroscopic dynamics. Specifically, torus bifurcations may occur in a single population of neurons without an external drive, serving as a crucial mechanism for the emergence of population bursting with two nested frequencies.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".