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Author Goles, E.; Montealegre, P.; Rios-Wilson, M. doi  openurl
  Title On The Effects Of Firing Memory In The Dynamics Of Conjunctive Networks Type
  Year 2020 Publication Discrete And Continuous Dynamical Systems Abbreviated Journal Discret. Contin. Dyn. Syst.  
  Volume 40 Issue 10 Pages 5765-5793  
  Keywords Discrete dynamical systems; boolean network; firing memory; conjunctive networks; prediction problem; and PSPACE  
  Abstract A boolean network is a map F : {0, 1}(n) -> {0, 1}(n) that defines a discrete dynamical system by the subsequent iterations of F. Nevertheless, it is thought that this definition is not always reliable in the context of applications, especially in biology. Concerning this issue, models based in the concept of adding asynchronicity to the dynamics were propose. Particularly, we are interested in a approach based in the concept of delay. We focus in a specific type of delay called firing memory and it effects in the dynamics of symmetric (non-directed) conjunctive networks. We find, in the caseis in which the implementation of the delay is not uniform, that all the complexity of the dynamics is somehow encapsulated in the component in which the delay has effect. Thus, we show, in the homogeneous case, that it is possible to exhibit attractors of non-polynomial period. In addition, we study the prediction problem consisting in, given an initial condition, determinate if a fixed coordinate will eventually change its state. We find again that in the non-homogeneous case all the complexity is determined by the component that is affected by the delay and we conclude in the homogeneous case that this problem is PSPACE-complete.  
  Address [Goles, Eric; Montealegre, Pedro] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Diagonal Torres 2650, Santiago, Chile, Email:;  
  Corporate Author Thesis  
  Publisher Amer Inst Mathematical Sciences-Aims Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1078-0947 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000545661800006 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1183  
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