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We study emergent dynamics of the discrete Cucker-Smale (in short, DCS) modelwith randomly switching network topologies. For this, we provide a sufficientframework leading to the stochastic flocking with probability one. Oursufficient framework is formulated in terms of an admissible set of networktopologies realized by digraphs and probability density function for randomswitching times. As examples for the law of switching times, we use the Poissonprocess and the geometric process and show that these two processes satisfy therequired conditions in a given framework so that we have a stochastic flockingwith probability one. As a corollary of our flocking analysis, we improve theearlier result [J.-G. Dong, S.-Y. Ha, J. Jung and D. Kim: On the stochasticflocking of the Cucker-Smale flock with randomly switching topologies.arXiv:1911.07390.] on the continuous C-S model.

Emergence of stochastic flocking for the discrete Cucker-Smale model with randomly switching topologies