Software ageing is correlated with available computing resources of the computer system. These available resources evolve with time, reflecting the developing mechanism of the ageing process. This study is the first to consider a degrading computer system as an evolving dynamic system. The authors proposed a non-linear dynamic model of software ageing, where the coefficients are estimated using a dynamic inversion method, and conduct controlled software experiments, where the experimental conditions are controlled to expedite ageing. The model can be used to forecast mutations of resource variables such as the buffer, cache and central processing unit usage, which have a direct impact on software performance. The stability of the model is assessed by the Jacobi matrix method, and the results show that, when part of a resource has become unallocable, the Linux operating system can readjust the resources to keep the system's performance stable. This process repeats until some of the resources are exhausted, when the system will crash or hang. This study provides hints on the ageing mechanism of computer systems, which are rarely reported in the past.