publication . Other literature type . Article . 2009

GLOBAL CONVERGENCE FOR THE XOR BOOLEAN NETWORKS

Juei-Ling Ho;
Open Access English
  • Published: 01 Aug 2009
  • Publisher: Mathematical Society of the Republic of China
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...
Subjects
arXiv: Computer Science::Computational Complexity
free text keywords: global convergent theorem, boolean network, discrete Jacobian matrix, boolean eigenvalue, fixed point, XOR boolean network, 37E15, 37E25, 68R99
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