发表机构
University of Toronto Institute for Aerospace Studies, University of Toronto; Department of Applied Mathematics and Centre for Theoretical Neuroscience, University of Waterloo（多伦多大学航空研究学院; 滑铁卢大学应用数学系与理论神经科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究首次为具有化学突触的Izhikevich神经元计算相位模型，分析锁相态稳定性及其与未耦合模型分岔的联系，并通过模拟验证预测。
AI 中文摘要
Izhikevich模型是一种计算高效的神经元模型，能够展现大脑中观察到的多种放电模式。然而，它是一个不连续的动力系统，这意味着为连续动力系统开发的弱耦合振荡器理论方法无法直接应用。因此，耦合Izhikevich模型的集体行为尚未得到充分研究。据我们所知，我们首次对具有化学突触的Izhikevich神经元模型进行了相位模型的计算。利用相位模型，我们研究了锁相态的存在性与稳定性，以及这些性质如何随参数变化。此外，我们发现相位模型的反相态稳定性与未耦合Izhikevich模型自身的分岔行为之间存在有趣的联系。相位模型预测的准确性通过两个弱耦合Izhikevich神经元的模拟得到了验证。
英文摘要
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.
Comments30 pages, 6 figures
