Effect of topological structure on synchronizability of network with connection delay

The effect of topological structure on synchronizability of network with connection delay is discussed in this paper. By introducing a new time variable in the master stability function, it is shown the effect of connection delay can be weakened when the maximum absolute value of the eigenvalues corresponding to the transverse directions is small. And then, on the basis of the results of local stability of time-delayed system, it is indicated that the network can achieve complete synchronization in larger region of the relevant bifurcation parameters when its outer-coupling matrix is with smaller maximum absolute value of the eigenvalues corresponding to the transverse directions. Numerical studies demonstrate the analytical finding.