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PreprintCC BY-SA 4.0arXiv

Stability of Phase-locked States of Weakly Coupled Izhikevich Neurons

  • XinYe Cheng
  • Sue Ann Campbell
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Abstract

The Izhikevich model is a computationally efficient neuron model that can exhibit a wide range of firing patterns observed in the brain. However, it is a discontinuous dynamical system, which means the methods for applying weakly coupled oscillator theory developed for continuous dynamical systems cannot be applied. Therefore, the collective behaviour of coupled Izhikevich model has not been fully studied. To our knowledge, we carry out the first computation of the phase model for an Izhikevich neuronal model with chemical synapses. Using the phase model we study the existence and stability of phase-locking states and how these vary with parameters. Moreover, we find an interesting connection between the stability of anti-phase states of the phase model and the bifurcation behaviour of the uncoupled Izhikevich model itself. The accuracy of the prediction of the phase model is supported by simulations of two weakly coupled Izhikevich neurons.

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Cite

BibTeXRIS
BibTeX
@misc{cheng2026stability,
  title = {{Stability of Phase-locked States of Weakly Coupled Izhikevich Neurons}},
  author = {XinYe Cheng and Sue Ann Campbell},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04025},
  eprint = {2610.04025},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04025},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Stability of Phase-locked States of Weakly Coupled Izhikevich Neurons
AU  - XinYe Cheng
AU  - Sue Ann Campbell
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.04025
UR  - https://arxiv.org/abs/2610.04025
AB  - The Izhikevich model is a computationally efficient neuron model that can exhibit a wide range of firing patterns observed in the brain. However, it is a discontinuous dynamical system, which means the methods for applying weakly coupled oscillator theory developed for continuous dynamical systems cannot be applied. Therefore, the collective behaviour of coupled Izhikevich model has not been fully studied. To our knowledge, we carry out the first computation of the phase model for an Izhikevich neuronal model with chemical synapses. Using the phase model we study the existence and stability of phase-locking states and how these vary with parameters. Moreover, we find an interesting connection between the stability of anti-phase states of the phase model and the bifurcation behaviour of the uncoupled Izhikevich model itself. The accuracy of the prediction of the phase model is supported by simulations of two weakly coupled Izhikevich neurons.
ER  -