The well-posedness and long term dynamics of a stochastic non-autonomous neural field lattice system on vector-valued indices \({\mathbb {Z}}^d\) driven by state dependent nonlinear noise are investigated in a weighted space of infinite sequences. First the existence and uniqueness of a mean square solution to the lattice system is established under the assumptions that the nonlinear drift and diffusion terms are component-wise continuously differentiable with weighted equi-locally bounded derivatives. Then the existence and uniqueness of a tempered weak pullback mean random attractor associated with the solution is proved. Finally the existence of invariant measures for the neural field lattice system is obtained by uniform tail-estimates and Krylov–Bogolyubov’s method.

在无限加权空间中研究了由状态相关非线性噪声驱动的向量值指数\ ({\ mathbb {Z}} ^ d \)上的随机非自治神经场格系统的适定性和长期动力学序列。首先，在非线性漂移和扩散项是分量方面连续可微的假设下，晶格系统的均方解的存在性和唯一性是通过加权等局域有界导数建立的。然后证明了与解相关的缓和弱回拉平均随机吸引子的存在性和唯一性。最后，通过均匀尾估计和 Krylov-Bogolyubov 方法获得了神经场格系统不变测度的存在性。