Taiwanese Journal of Mathematics

GLOBAL CONVERGENCE FOR THE XOR BOOLEAN NETWORKS

Juei-Ling Ho

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Abstract

Shih and Ho have proved a global convergent theorem for boolean network: if a map from $\{0,1\}^{n}$ to itself defines a boolean network has the conditions: (1) each column of the discrete Jacobian matrix of each element of $\{0,1\}^{n}$ is either a unit vector or a zero vector; (2) all the boolean eigenvalues of the discrete Jacobian matrix of this map evaluated at each element of $\{0,1\}^{n}$ are zero, then it has a unique fixed point and this boolean network is global convergent to the fixed point. The purpose of this paper is to give a global convergent theorem for XOR boolean network, it is a counterpart of the global convergent theorem for boolean network.

Article information

Source
Taiwanese J. Math., Volume 13, Number 4 (2009), 1271-1282.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405507

Digital Object Identifier
doi:10.11650/twjm/1500405507

Mathematical Reviews number (MathSciNet)
MR2543742

Zentralblatt MATH identifier
1180.37052

Subjects
Primary: 37E15: Combinatorial dynamics (types of periodic orbits) 37E25: Maps of trees and graphs 68R99: None of the above, but in this section

Keywords
global convergent theorem boolean network discrete Jacobian matrix boolean eigenvalue fixed point XOR boolean network

Citation

Ho, Juei-Ling. GLOBAL CONVERGENCE FOR THE XOR BOOLEAN NETWORKS. Taiwanese J. Math. 13 (2009), no. 4, 1271--1282. doi:10.11650/twjm/1500405507. https://projecteuclid.org/euclid.twjm/1500405507


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References

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