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 -