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Discrete, sequential dynamical systems
, 2001
"... We study a class of discrete dynamical systems that consists of the following data: (a) a finite loopfree graph Y with vertex set {1;:::;n} where each vertex has a binary state, (b) a vertex labeled multiset of functions (Fi;Y: F n 2 → F n 2)i and (c) a permutation ∈Sn. The function Fi;Y updates t ..."
Abstract

Cited by 23 (7 self)
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We study a class of discrete dynamical systems that consists of the following data: (a) a finite loopfree graph Y with vertex set {1;:::;n} where each vertex has a binary state, (b) a vertex labeled multiset of functions (Fi;Y: F n 2 → F n 2)i and (c) a permutation ∈Sn. The function Fi;Y updates the state of vertex i as a function of the states of vertex i and its Yneighbors and leaves the states of all other vertices fixed. The permutation represents a Yvertex ordering according to which the functions Fi;Y are applied. By composing the functions Fi;Y in the order given by we obtain the dynamical system [FY;] = � n i=1 F (i);Y: F n 2 → F n 2; which we refer to as a sequential dynamical system (SDS). Among various basic results on SDS we will study their invertibility and analyze the set {[FY; ]  ∈Sn}  for xed Y and (Fi;Y)i. Finally, we give an estimate for the number of nonisomorphic digraphs [FY; ] (having vertex sets F n 2 and directed edges {(x; [FY;](x)) x ∈ F n 2}) for a xed graph Y and a fixed multiset (Fi;Y)i.