Enumeration of homogeneous coupled cell networks
UNSPECIFIED. (2005) Enumeration of homogeneous coupled cell networks. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 15 (8). pp. 2361-2373. ISSN 0218-1274Full text not available from this repository.
A coupled cell network is a schematic diagram employed to define a class of differential equations, and can be thought of as a directed graph whose nodes (cells) represent dynamical systems and whose edges (arrows) represent couplings. Often the nodes and edges are labeled to distinguish different types of system and coupling. The associated differential equations reflect this structure in a natural manner. The network is homogeneous if there is one type of cell and one type of arrow, and moreover, every cell lies at the head end of the same number of arrows. This number is the valency of the network. We use a group-theoretic formula usually but incorrectly attributed to William Burnside to enumerate homogeneous coupled cell networks with N cells and valency r, in both the disconnected and connected cases. We compute these numbers explicitly when AF. r <= 6.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
|Journal or Publication Title:||INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS|
|Publisher:||WORLD SCIENTIFIC PUBL CO PTE LTD|
|Official Date:||August 2005|
|Number of Pages:||13|
|Page Range:||pp. 2361-2373|
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