TY - JOUR
T1 - On the effects of firing memory in the dynamics of conjunctive networks
AU - Goles, Eric
AU - Montealegre, Pedro
AU - Riós-Wilson, Martín
N1 - Publisher Copyright:
© 2020 American Institute of Mathematical Sciences. All rights reserved.
PY - 2020/10
Y1 - 2020/10
N2 - 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.
AB - 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.
KW - Boolean network
KW - Conjunctive networks
KW - Discrete dynamical systems
KW - Firing memory
KW - Prediction problem
KW - and PSPACE
UR - http://www.scopus.com/inward/record.url?scp=85088095576&partnerID=8YFLogxK
U2 - 10.3934/dcds.2020245
DO - 10.3934/dcds.2020245
M3 - Article
AN - SCOPUS:85088095576
SN - 1078-0947
VL - 40
SP - 5765
EP - 5793
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
IS - 10
ER -