We consider a recurrent network of two oscillatory neurons that are coupled with inhibitory synapses. We use the phase response curves of the neurons and the properties of short-term synaptic depression to define Poincaré maps for the activity of the network. The fixed points of these maps correspond to phase-locked modes of the network. Using these maps, we analyze the conditions that allow short-term synaptic depression to lead to the existence of bistable phase-locked, periodic solutions. We show that bistability arises when either the phase response curve of the neuron or the short-term depression profile changes steeply enough. The results apply to any Type I oscillator and we illustrate our findings using the Quadratic Integrate-and-Fire and Morris–Lecar neuron models.

我们考虑两个抑制性突触耦合的振荡神经元的递归网络。我们使用神经元的相位响应曲线和短期突触抑制的特性来定义网络活动的庞加莱图。这些图的固定点对应于网络的锁相模式。使用这些图，我们分析了允许短期突触抑制导致双稳态锁相周期解的存在的条件。我们表明，当神经元的相位响应曲线或短期抑郁曲线变化足够陡峭时，就会出现双稳态。结果适用于任何I型振荡器，我们使用二次积分和发射和Morris-Lecar神经元模型来说明我们的发现。