Simulation and sequential dynamical systems

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Computer simulations have a generic structure. Motivated by this the authors present a new class of discrete dynamical systems that captures this structure in a mathematically precise way. This class of systems consists of (1) a loopfree graph {Upsilon} with vertex set {l_brace}1,2,{hor_ellipsis},n{r_brace} where each vertex has a binary state, (2) a vertex labeled set of functions (F{sub i,{Upsilon}}:F{sub 2}{sup n} {yields} F{sub 2}{sup n}){sub i} and (3) a permutation {pi} {element_of} S{sub n}. The function F{sub i,{Upsilon}} updates the state of vertex i as a function of the states of vertex i and its {Upsilon}-neighbors and leaves the states ... continued below

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9 pages

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Mortveit, H.S. & Reidys, C.M. June 1, 1999.

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Description

Computer simulations have a generic structure. Motivated by this the authors present a new class of discrete dynamical systems that captures this structure in a mathematically precise way. This class of systems consists of (1) a loopfree graph {Upsilon} with vertex set {l_brace}1,2,{hor_ellipsis},n{r_brace} where each vertex has a binary state, (2) a vertex labeled set of functions (F{sub i,{Upsilon}}:F{sub 2}{sup n} {yields} F{sub 2}{sup n}){sub i} and (3) a permutation {pi} {element_of} S{sub n}. The function F{sub i,{Upsilon}} updates the state of vertex i as a function of the states of vertex i and its {Upsilon}-neighbors and leaves the states of all other vertices fixed. The permutation {pi} represents the update ordering, i.e., the order in which the functions F{sub i,{Upsilon}} are applied. By composing the functions F{sub i,{Upsilon}} in the order given by {pi} one obtains the dynamical system (equation given in paper), which the authors refer to as a sequential dynamical system, or SDS for short. The authors will present bounds for the number of functionally different systems and for the number of nonisomorphic digraphs {Gamma}[F{sub {Upsilon}},{pi}] that can be obtained by varying the update order and applications of these to specific graphs and graph classes.

Physical Description

9 pages

Notes

OSTI as DE00353452

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  • GECCO '99 conference, Orlando, FL (US), 07/14/1999--07/17/1999; Other Information: Supercedes report DE99002829; PBD: [1999]

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  • Other: DE99002829
  • Report No.: LA-UR--99-561
  • Report No.: CONF-990703--
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 353452
  • Archival Resource Key: ark:/67531/metadc687793

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  • June 1, 1999

Added to The UNT Digital Library

  • July 25, 2015, 2:20 a.m.

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  • Feb. 26, 2016, 5:41 p.m.

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Mortveit, H.S. & Reidys, C.M. Simulation and sequential dynamical systems, article, June 1, 1999; New Mexico. (digital.library.unt.edu/ark:/67531/metadc687793/: accessed July 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.