There is also such a thing as a logical system. The most obvious example is the calculus developed simultaneously by Leibniz and Isaac Newton. Another example is George Boole's Boolean operators. Other examples have related specifically to philosophy, biology, or cognitive science.
Maslow's Hierarchy of Needs applies psychology to biology by using pure logic. Numerous psychologists, including Carl Jung and Sigmund Freud have developed systems which logically organize psychological domains, such as personalities, motivations, or intellect and desire.
A system is a set of interacting or interdependent component parts forming a complex/intricate whole.
Every system is delineated by its spatial and temporal boundaries, surrounded and influenced by its environment, described by its structure and purpose and expressed in its functioning.