A system can be considered as a collection of entities and their interrelationships gathered together to form a whole greater than the sum of the entities. The interactions can be represented by simple rules that describe how the state of any entity in the system is dependent on the state of its neighbors.
The domain of investigation of systems science consists of properties of systems and associated problems which emanate from the notion of system-hood. Due to the growing complexity of systems, the need of studying systems science is utmost important and significant. In particular, to deal with variety of situations in communication systems, ecological systems, physical systems, social systems, that appear today, the fast growing use of mathematical and statistical methods can be observed. This calls for the development of systematic sophisticated conceptual framework of mathematical and statistical methods that helps understanding the behavior of complex systems, and identifying the system-hood properties of a real system. Moreover, the subtle mathematical abstraction also can gainfully be extended to design new complex systems that may overcome the difficulty of a state of affairs.
As per the historical notion, Mathematics has been playing a key role in realizing, describing and dealing with systems in almost every areas of science and engineering. The need of new mathematical tools and techniques in systems science is a challenging chore. Further, due to the emergence of systems movement in some areas of engineering and management, for example, designing engineering systems of rapidly increasing complexity and decision making in complex organizations, it becomes more important to think in terms of systems. Systems engineering and systems analysis become the core to determine the evolution of systems movement, and Mathematics plays an important role to critically analyze and understand the same.
Following are a few of the major concerns that drive the systems science research at CoE in SS:
The CoE in SS aims to facilitate the development and use of Mathematical techniques in verities of situations that appear in Social-ecological systems, Physical systems, Fundamental Complex Systems, Communication Systems. The CoE also intends to provide the concept of "systems thinking" that enables one to solve complex problems which involve visualizing the "broad picture" and not just their parts. The focus areas of the CoE include, but not limited to,