Finite-time synchronization of multi-weighted complex dynamical networks with and without coupling delay

Two kinds of multi-weighted complex dynamical networks models with and without coupling delay are respectively considered in this paper. First of all, a finite-time synchronization criterion which ensures that multi-weighted complex dynamical networks with fixed topology and constant coupling realize synchronization in finite time is established by means of Lyapunov functional and state feedback controllers. On the basis of Dini derivative and some inequality techniques, a sufficient condition which guarantees synchronization in finite time of multi-weighted complex dynamical networks with switching topology and constant coupling is acquired. On the other hand, in view of the research results above, we similarly investigate multi-weighted complex dynamical networks with time delayed coupling. Two numerical examples finally are provided to verify the availability of the proposed results.