GLOBAL CONVERGENCE FOR THE XOR BOOLEAN NETWORKS

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.