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Criterion of complete chaos synchronization for diverse three-node VCSEL networks with coupling

For diverse three node vertical-cavity surface-emitting laser (VCSEL) networks with uniform time-delayed coupling, we propose a new criterion of the globally complete chaos synchronization (GCCS) among all node lasers by using the mater-stability function (MSF). It is found that GCCS can be achieved for an arbitrarily given three-node VCSEL networks when two points determined by constant row sum and two transversal eigenvalues fall into the region of stability where maximum Lyapunov exponent (MLE) is negative and the MLE as a function of constant row sum and the eigenvalue associated to perturbations within the synchronization manifold is positive.