Type of Document Master's Thesis Author Boquet, Grant Michael Author's Email Address email@example.com URN etd-03232008-175232 Title Multidimensional Behavioral Complexes Degree Master of Science Department Mathematics Advisory Committee
Advisor Name Title Ball, Joseph A. Committee Chair Haskell, Peter E. Committee Member Linnell, Peter A. Committee Member Keywords
- multidimensional systems theory
- Behavioral systems theory
Date of Defense 2008-03-19 Availability unrestricted AbstractIn a preprint by J. Wood, V. Lomadze, and E. Rogers, chains and boundary maps were defined for 2-D discrete behavioral systems. The corresponding homology groups were studied and tied to trajectory properties. Indeed, the homology groups encapsulated the concepts of autonomy, controllability, and signal restriction.
We shall present an extension of their work to n-D discrete behavioral systems. In particular, we shall streamline the construction of the chain groups, the boundary maps between chains, and the study of the resultant homology groups. While constructing this machinery, we shall point out intrinsic flaws in their approach that make extension of their results less systematic. Finishing remarks shall be made on using the homology groups to determine system properties and potentially classify forms of controllability.
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