All equilibrium is temporary and imperfect. In the complete absence of external influences (which in the extreme in practice is impossible) ecosystems do indeed reach something approaching equilibrium, certainly with fluctuations in predators and prey, but no violent, sudden disruptions.

There's a whole genre of YouTube videos made by hobbyists who establish ecosystems in glass jars and seal them for many years.

https://youtu.be/Es6DDuMmhAM

Edit: With (of course) the external influence of light ;)