AI 中文总结
该研究提出带大象型记忆的有限随机脉冲神经元网络，证明其相关动力学性质，发现大象记忆影响放电与灭绝行为，复制平均场近似可匹配其有限网络动力学。
AI 中文摘要
我们引入一种具有大象型记忆的有限随机脉冲神经元网络，其中过往的放电活动通过依赖强化的阈值改变未来的兴奋性。对于有界硬阈值放电率，我们证明了该有限系统不会爆炸，并在截断势空间上的1-瓦瑟斯坦距离中得到条件指数收缩。随后我们构建了对应的复制平均场动力学，证明了该非线性过程的整体存在性、律的唯一性及非爆炸性质，并刻画了其不变测度。数值实验表明，大象记忆会使放电活动产生依赖p的下降、改变灭绝行为，且复制平均场近似能很好匹配有限网络的动力学。
英文摘要
We introduce a finite stochastic spiking-neuron network with Elephant-type memory, in which past firing activity modifies future excitability through a reinforcement-dependent threshold. For a bounded hard-threshold firing rate, we prove non-explosion of the finite system and obtain conditional exponential contraction in (1)-Wasserstein distance on a truncated potential space. We then formulate the corresponding replica mean-field dynamics and establish global existence, uniqueness in law, and non-explosion of the nonlinear process, together with a characterization of its invariant measures. Numerical experiments show that Elephant memory produces a (p)-dependent decline in firing activity, alters extinction behaviour, and yields finite-network dynamics closely matched by the replica mean-field approximation.
