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.
Citation
Juei-Ling Ho. "GLOBAL CONVERGENCE FOR THE XOR BOOLEAN NETWORKS." Taiwanese J. Math. 13 (4) 1271 - 1282, 2009. https://doi.org/10.11650/twjm/1500405507
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