# brain: stability of phase-locked states of weakly coupled Izhikevich neurons.

<< ️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 (Their) knowledge, (AA) carry out the first computation of the phase model for an Izhikevich neuronal model with chemical synapses. Using the phase model (They) study the existence and stability of phase-locking states and how these vary with parameters. >>

<< ️Moreover, (AA) 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. >>

XinYe Cheng, Sue Ann Campbell. Stability of Phase-locked States of Weakly Coupled Izhikevich Neurons. arXiv: 2610.04025v1 [q-bio.NC]. Oct 2, 2026.

https://arxiv.org/abs/2610.04025

Also: brain, neuro, behav, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, brain, behavior, collective behavior, weakly coupled oscillator theory, phase models, phase-locking states, synchronization, bifurcations, discontinuous bifurcations.