The rapid eye movements (saccades) used to transfer gaze between targets are examples of an action. The behaviour of saccades matches that of the slow–fast model of actions originally proposed by Zeeman. Here, we extend Zeeman’s model by incorporating an accumulator that represents the increase in certainty of the presence of a target, together with an integrator that converts a velocity command to a position command. The saccadic behaviour of several foveate species, including human, rhesus monkey and mouse, is replicated by the augmented model. Predictions of the linear stability of the saccadic system close to equilibrium are made, and it is shown that these could be tested by applying state-space reconstruction techniques to neurophysiological recordings. Moreover, each model equation describes behaviour that can be matched to specific classes of neurons found throughout the oculomotor system, and the implication of the model is that build-up, burst and omnipause neurons are found throughout the oculomotor pathway because they constitute the simplest circuit that can produce the motor commands required to specify the trajectories of motor actions.

用于在目标之间转移目光的快速眼球运动（扫视）就是动作的示例。眼跳的行为与塞曼最初提出的慢-快动作模型相匹配。在这里，我们通过合并代表目标存在确定性增加的累加器以及将速度命令转换为位置命令的积分器来扩展塞曼模型。增强模型复制了包括人类、恒河猴和小鼠在内的几种中心凹物种的扫视行为。对扫视系统接近平衡的线性稳定性进行了预测，并且表明可以通过将状态空间重建技术应用于神经生理学记录来测试这些预测。此外，每个模型方程描述了可以与整个动眼神经系统中发现的特定神经元类别相匹配的行为，该模型的含义是在整个动眼神经通路中发现了累积、爆发和全停神经元，因为它们构成了最简单的电路它可以产生指定电机动作轨迹所需的电机命令。