In this article, we study the quasi-synchronization problems in multiplex networks under deception attacks. First, we propose a new model of multiplex networks with interlayer couplings under deception attacks. We assume that the attackers inject false data into the communication channels. Since interlayer couplings are taken into account, we consider not only the case where attacks occur in the intralayer channels, but also the case where attacks occur in the interlayer communication channels. Furthermore, we set two binary variables obeying a random Bernoulli distribution to characterize whether the attacks occur or not. We then design an impulsive controller to enable the nodal states to achieve the desired states. By means of the Lyapunov function method and the average impulsive interval method, we obtain the sufficient conditions under which the nodal states can achieve interlayer quasi-synchronization and intralayer quasi-synchronization, respectively. Naturally, we obtain the sufficient conditions under which the nodal states can achieve complete quasi-synchronization. Furthermore, we introduce a leader and design a different impulsive controller. Using the same theoretical approach, we derive the sufficient conditions under which the nodal states can achieve complete quasi-synchronization. Finally, we provide three numerical examples to confirm the theoretical results.
Jin et al. (Thu,) studied this question.