Central and state governments influence each other in What system

The correct answer is a federal system

A federal system is found in a federation. It's an organization in which numerous states who have their own local governments also have a federal government that provides laws for the entire federation. Everything not decided by the federal government can be made into law by the local state government as long as it adheres to federation principles and laws.

Central and state governments influence each other in what is known as a "federation" or sometimes a republic, although the true definition is "federation".