Flocking of non-identical Cucker-Smale models on general coupling network

The purpose of the paper is to investigate flocking behavior discrete-time Cucker-Smale(C-S) model under general interaction network topologies with agents having their free-will accelerations. We prove theoretically that if accelerations are summable, then, for any given initial conditions, solution achieves a finite moving speed by suitably choosing time step as well communication rate system or strength between agents. In particular, \begin{document}$ \beta $\end{document} subcritical, i.e., less than critical value \beta_c , then holds conditions regardless While, ( = ) supercritical > ), can only be achieved making large enough. also present some numerical simulations support our obtained theoretical results.