Synchronization of networked harmonic oscillators subject to Markovian jumping coupling strengths

To explore the effect the switching coupling strengths on synchronization of complex dynamical networks, both an impulsive coupling protocol and a piecewise constant coupling protocol are designed by using periodic sampling velocity data for a group of harmonic oscillators. Moreover, the convergence of these protocols with switching coupling strengths is discussed and some sufficient conditions are established under which the networked harmonic oscillators could achieve collective oscillatory behavior in almost sure sense. It is shown that the almost sure exponential synchronization can be reached even when the coupling strength is switched between enabling and not enabling to achieve synchronization. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.