过去三十年间，一种被称为超离散化（ultradiscretisation）的特殊极限过程，已成为无穷维可积系统领域中构造具有孤子行为的元胞自动机（如Korteweg-de Vries方程所描述的情形）的首选工具。一个较少为人知的事实是，在许多情况下，超离散化亦可用于构造保留常微分方程（ODE）所描述的动力系统之核心动力学特征（例如极限环的存在性等）的元胞自动机。在标准应用中，超离散化过程依赖于预先构造一个‘良好’的离散化模型——该模型须与原ODE共享核心动力学特征，且符号恒定（sign-free），从而可施行超离散极限。本文以一个简单但具代表性的模型为例表明：即使起始的离散系统与其连续极限（即对应ODE）具有不同的动力学特征，仍可通过调整超离散极限过程，使所得元胞自动机的动力学行为更接近其连续极限，而非原始离散模型本身。

Over the past 30 years, the special limiting procedure known as ultradiscretisation has become the tool of choice in the field of infinite dimensional integrable systems for constructing cellular automata that exhibit solitonic behaviour, as e.g. in the Korteweg-de Vries equation. A lesser known fact is that, in many cases, ultradiscretisation can also be used to construct cellular automata that retain the essential dynamical features (such as the existence of limit cycles etc.) of a dynamical system expressed in terms of ordinary differential equations (ODEs). In its standard application, the ultradiscretisation procedure relies on the prior construction of a `good' discretisation of the dynamical system at hand, that shares the essential dynamical features of the ODE and which is sign-free, making it amenable to the ultradiscrete limit. In this paper we show, on a simple but generic model, that even if one starts from a discrete system with different dynamical features than the ODE one obtains as its continuum limit, the ultradiscrete limit can be tweaked such that the dynamics of the resulting cellular automaton is closer to that of the continuum limit than to that of the discrete model itself.