Traditional synaptic plasticity experiments and models depend on tight temporal correlations between pre- and postsynaptic activity. These tight temporal correlations, on the order of tens of milliseconds, are incompatible with significantly longer behavioral time scales, and as such might not be able to account for plasticity induced by behavior. Indeed, recent findings in hippocampus suggest that rapid, bidirectional synaptic plasticity which modifies place fields in CA1 operates at behavioral time scales. These experimental results suggest that presynaptic activity generates synaptic eligibility traces both for potentiation and depression, which last on the order of seconds. These traces can be converted to changes in synaptic efficacies by the activation of an instructive signal that depends on naturally occurring or experimentally induced plateau potentials. We have developed a simple mathematical model that is consistent with these observations. This model can be fully analyzed to find the fixed points of induced place fields and how these fixed points depend on system parameters such as the size and shape of presynaptic place fields, the animal's velocity during induction, and the parameters of the plasticity rule. We also make predictions about the convergence time to these fixed points, both for induced and pre-existing place fields.

传统的突触可塑性实验和模型依赖于突触前和突触后活动之间的紧密时间相关性。这些紧密的时间相关性（大约数十毫秒）与明显更长的行为时间尺度不相容，因此可能无法解释行为引起的可塑性。事实上，最近在海马体中的发现表明，改变 CA1 位置场的快速双向突触可塑性在行为时间尺度上发挥作用。这些实验结果表明，突触前活动会产生增强和抑制的突触资格痕迹，持续时间约为几秒。通过激活取决于自然发生或实验诱导的平台电位的指导信号，这些痕迹可以转化为突触功效的变化。我们开发了一个与这些观察结果一致的简单数学模型。可以对该模型进行全面分析，以找到感应位置场的固定点以及这些固定点如何依赖于系统参数，例如突触前位置场的大小和形状、感应过程中动物的速度以及可塑性规则的参数。我们还对诱导位置场和预先存在的位置场的这些固定点的收敛时间进行预测。