Synchronization in oscillator networks with coupling balance

Under the hypothesis of coupling balance, both locally and globally asymptotically synchronization of oscillator networks with nonlinear coupling in general form are studied for the first time. In order to study the globally asymptotically synchronization, we first show that the oscillator network is eventually dissipative if the uncoupled oscillators are eventual dissipative. Then in its absorbing domain, two methods developed recently are combined to study the asymptotically synchronization and two theorems are derived. Numerical simulations confirm the validity of the results.