In philosophical studies regarding mathematical models of dynamical systems, instability due to sensitive dependence on initial conditions, on the one side, and instability due to sensitive dependence on model structure, on the other, have by now been extensively discussed. Yet there is a third kind of instability, which by contrast has thus far been rather overlooked, that is also a challenge for model predictions about dynamical systems. This is the numerical instability due to the employment of numerical methods involving a discretization process, where discretization is required to solve the differential equations of dynamical systems on a computer. We argue that the criteria for numerical stability, as usually provided by numerical analysis textbooks, are insufficient, and, after mentioning the promising development of backward analysis, we discuss to what extent, in practice, numerical instability can be controlled or avoided.

在关于动力系统数学模型的哲学研究中，一方面，一方面敏感地依赖于初始条件，另一方面，由于敏感地依赖于模型结构而引起的不稳定性，现在已经得到了广泛的讨论。然而，存在第三种不稳定性，相比之下，到目前为止，这种不稳定性被忽略了，这对于动力学系统的模型预测也是一个挑战。这是由于使用涉及离散化的数值方法而导致的数值不稳定性，其中需要离散化才能在计算机上求解动力学系统的微分方程。我们认为数值稳定性的标准正如通常由数值分析教科书提供的那样，这是不够的，并且在提到向后分析的发展前景之后，我们讨论了在实践中可以控制或避免数值不稳定性的程度。