Synchronous Behavior of Coupled Oscillatory Network with Different Interconnection Patterns

Abstract

This paper concerns with the synchronous behavior of coupled oscillatory networks with positive and negative interconnections. Furthermore, the coupling strength is related to the frequencies of oscillators, and we study the dynamical behavior of power networks with weight coefficient between oscillators. Most importantly, time delay is inevitable in the propagation power through the transmission line. Thus, the impact of time delay on synchronous state of oscillatory network is discussed. Simulation results show that the impact of positive interconnection is not obvious on the synchronous state of power network. Nevertheless, for negative coupling, large coupling strength between oscillators decreases the synchronous performance. In addition, we find that when the weight coefficient is even, the synchronous ability of network increases with the increase in weight coefficient whatever the coupling strategy and topological structure be. However, when weight parameter is odd, the entire network with negative coupling cannot achieve synchronization. Finally, our results show that time delay has a critical value $\tau =1$ , and the evolutions of order parameters are different under different values of time delay.