In this article, we introduce a system of non-linear inverse mixed variational inequalities (SNIMVIs). We propose a proximal neurodynamic model (PNDM) for solving SNIMVIs, leveraging proximal mappings. The uniqueness of the continuous solution for the PNDM is proved by assuming Lipschitz continuity. Moreover, we establish the global asymptotic stability of equilibrium points of the PNDM, contingent upon Lipschitz continuity and strong monotonicity. Additionally, an iterative algorithm involving proximal mappings for solving the SNIMVIs is presented. Finally, we provide illustrative examples to support our main findings. Furthermore, we provide an example where the SNIMVIs violate the strong monotonicity condition and exhibit the divergence nature of the trajectories of the corresponding PNDM.

中文翻译：

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非线性逆混合变分不等式系统的近端神经动力学模型

在本文中，我们介绍了非线性逆混合变分不等式（SNIMVI）系统。我们提出了一种利用近端映射来解决 SNIMVI 的近端神经动力学模型 (PNDM)。通过假设 Lipschitz 连续性证明了 PNDM 连续解的唯一性。此外，我们根据 Lipschitz 连续性和强单调性建立了 PNDM 平衡点的全局渐近稳定性。此外，还提出了一种涉及近端映射的迭代算法来求解 SNIMVI。最后，我们提供说明性示例来支持我们的主要发现。此外，我们提供了一个例子，其中 SNIMVI 违反了强单调性条件并表现出相应 PNDM 轨迹的发散性质。