Algorithms for Analyzing Generalized Cell Mappings

Abstract

In the last chapter we discussed the basic ideas of the theory of generalized cell mapping and some elements of the theory of Markov chains. From the discussion it is obvious that if a normal form of the transition probability matrix can be found, then a great deal of the system behavior is already on hand. To have a normal form (10.3.7) is essentially to know the persistent groups and the transient groups. In Section 10.5 we have seen some simple examples of generalized cell mapping. Those examples involve only a very small number of cells. The normal forms can be obtained merely by inspection. For applications of generalized cell mapping to dynamical systems where a very large number of cells are used, it is an entirely different matter. We need a viable procedure to discover persistent and transient groups and, if possible, the hierarchy among the transient groups.