On The Effects Of Firing Memory In The Dynamics Of Conjunctive Networks
Goles
E
author
Montealegre
P
author
Rios-Wilson
M
author
2020
English
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.
Discrete dynamical systems
boolean network
firing memory
conjunctive networks
prediction problem
and PSPACE
WOS:000545661800006
exported from refbase (show.php?record=1183), last updated on Sat, 01 Aug 2020 14:55:33 -0400
text
10.3934/dcds.2020245
Goles_etal2020
Discrete And Continuous Dynamical Systems
Discret. Contin. Dyn. Syst.
2020
Amer Inst Mathematical Sciences-Aims
continuing
periodical
academic journal
40
10
5765
5793
1078-0947