The two constructions follow the forms below

• the form:

• impact on

impact in The President has an impact on world politics.

Whereworld politics is the object of impact.

Can the President be influential in the world politics?

Where do world politics fit in? In world politics, the president has an impact. What makes the difference?

The object of impact is unknown. And noting that the object of impact is unlikely.

In the OP’s examples, because there is no phrase indicating that system behavior is being used as context or scope, the native English speaker would assume it to be an object and use on.