Numerical instability and dynamical systems

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