1. The complexity of a problem arises when a value of the parameter a is large.
2. The complexity of a problem increases with an increasing value of the parameter a.
Which one is better/correct? I would prefer the second meaning (as the two sentences have slightly different meaning IMO) but am not sure whether it is a correct sentence or not.
The complexity of a problem rises when the value of the X parameter is large.
This sentence is talking about any instance of a problem that involves the X parameter; a large value for that parameter makes the complexity of such a problem rise.
One could also say
The complexity of a problem rises when the value of the parameter X is large.
But when talking about a particular problem, where the X parameter has a certain value,
The complexity of the problem rises because the value of parameter X is large.
I think the articles you've seen are referring to particular problems.
Thanks, BobK. And practice you brain because many parameters in mathematics has a symbol "a", and avoiding it would be just confusing for those who know the parameter.