There are many correct answers to this question, as their are many characteristics of a stable ecosystem. An ecosystem is defined as a community of organisms interacting with one another. An ecosystem is stable with the organisms and non-living parts of it are in equillibrium.
When this happens nutrients are cycled correctly and other organisms are unable to interrupt the flow. It is also stable when the ecosystem is able to use sunlight for energy. Along with that, an stable ecosystem happens when waste is handled properly. When it is disposed, nutrients are replenished by recycling. Lastly, an ecosystem is stable with the maintain of biodiversity.