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

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 using the mater-stability function (MSF). Here, the MSF can be obtained by calculating the maximum Lyapunov exponent (MLE) and MLE is calculated from the modified master stability equation. Note that the outer-coupling matrixes have a nonzero row sum (nondiffusive coupling) and the inner-coupling is a function of the self-node and delay connection node. It is found that GCCS can be achieved for an arbitrarily given three-node VCSEL networks when two points determined by the constant row sum and two transversal eigenvalues fall into the region of stability where MLE is negative and the MLE as a function of the constant row sum and the eigenvalue associated to perturbations within the synchronization manifold is positive. Based on the theoretical criterion and synchronization error theory, we further explore the synchronization properties in three-node VCSEL networks with the ring topology and that with the bus topology. As a result, the theoretical criterion is in excellent agreement with our numerical results, which indicate that the theoretical criterion is valid and feasible.