Zeroing neural dynamics (ZND), a special class of neural dynamics, is a powerful methodology for time-varying problems solving. On the basis of this methodology, different continuous-time ZND models are obtained for various time-varying problems solving. Continuous-time ZND models are supposed to be discretized for the sake of prevalent digital-equipment applications, and a discretization formula is needed to transform a continuous-time ZND model into a discrete-time ZND model. In this article, continuous-time ZND models, new discretization formulas and various discrete-time ZND models are presented. The time-varying minimization problem, which is a representative time-varying issue, is also discussed as an example throughout this article. The relationship between ZND and Zhao-Lu-Swamy-Feng (ZLSF) models is identified; i.e., the ZLSF models are minimization-type and Euler-type special cases of ZND models. In addition, ZND models are compared with other models to demonstrate their differences. The article aims to introduce the ZND methodology and illustrate the manner by which it is used, provide readers with new discretization formulas and various continuous-time and discrete-time ZND models for time-varying problems solving, discuss the factors affecting the performance of the aforementioned models, exemplify the differences between ZND models and other models, and point out future research directions.

中文翻译：

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用 ZLSF 模型作为最小化型和欧拉型特例求解各种时变问题的归零神经动力学和模型 [研究前沿]

归零神经动力学 (ZND) 是一类特殊的神经动力学，是解决时变问题的强大方法。在此方法的基础上，针对各种时变问题求解，得到了不同的连续时间ZND模型。为了普遍的数字设备应用，连续时间ZND模型应该被离散化，并且需要一个离散化公式将连续时间ZND模型转化为离散时间ZND模型。本文介绍了连续时间 ZND 模型、新的离散化公式和各种离散时间 ZND 模型。时变最小化问题是一个具有代表性的时变问题，在本文中也作为示例进行了讨论。确定了 ZND 和 Zhao-Lu-Swamy-Feng (ZLSF) 模型之间的关系；IE，ZLSF 模型是 ZND 模型的最小化型和欧拉型特例。此外，将 ZND 模型与其他模型进行比较以展示它们的差异。本文旨在介绍 ZND 方法并说明其使用方式，为读者提供新的离散化公式和各种连续时间和离散时间 ZND 模型来解决时变问题，讨论影响该方法性能的因素。上述模型，举例说明ZND模型与其他模型的区别，并指出未来的研究方向。