Analytic Treatment of the Network Synchronization Problem with Time Delays

作者：Hod Shahar^*

来源：Physical Review Letters, 2010, 105(20): 208701.

DOI：10.1103/PhysRevLett.105.208701

Motivated by novel results in the theory of network synchronization, we analyze the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. We determine analytically the fundamental limit of synchronization efficiency in a noisy environment with uniform time delays. We show that the optimal efficiency of the network is achieved for lambda tau = pi(3/2)/2 root pi+4 approximate to 0.738, where lambda is the coupling strength (relaxation coefficient) and tau is the characteristic time delay in the communication between pairs of nodes. Our analysis reveals the underlying mechanism responsible for the trade-off phenomena observed in recent numerical simulations of network synchronization problems.

• 出版日期2010-11-9