Bipartite Flocking for Cucker-Smale Model on Cooperation-Competition Networks Subject to Denial-of-Service Attacks

This work emphasises the bipartite flocking of leader-follower Cucker-Smale model on cooperation-competition networks under Denial-of-Service (DoS) attacks. The DoS with limited energy is the periodic signal that consists of active periods and asleep periods. It interruptes the information interactions among agents during the activation stages, while it concentrates on storing own energy for the next attack moment during the asleep stages. Meanwhile, the control strategy to defend against DoS attacks is established. The products convergence of infinite sub-stochastic matrices method is employed to implement the bipartite flocking behavior. Based on this method, a algebraic condition which is related to initial states, the topological structure and the weight function is constructed. Moreover, the obtained theoretical results are demonstrated by numerical simulations.