Periodic consensus in network systems with general distributed processing delays

How to understand the dynamical consensus patterns in network systems is of particular significance both theories and applications. In this paper, we are interested investigating influences distributed processing delay on a model. As new observations, show that desired model undergoes weak periodic behaviors when parameters reach threshold value connectedness system may be absent. results, some criterions with exponential convergent rate established by standard functional differential equations analysis. An analytic formula given calculate asymptotic terms initial time interval. Also, post values for typical distributions included uniform distribution Gamma distribution. Finally, give numerical simulation analyse different delays consensus.