Cluster synchronization control for coupled genetic oscillator networks under denial-of-service attacks: Pinning partial impulsive strategy

This paper focuses on the security cluster synchronization (CS) of coupled genetic oscillator networks (GONs) with parameters mismatch under denial-of-service (DoS) attacks. Firstly, a model of DoS attacks on the control channel of GONs is established. Then, in order to achieve secure CS of GONs under DoS attacks, a pinning partial impulsive control (PPIC) strategy is proposed for the first time. Compared with the existing pinning impulsive control and partial impulsive control, the PPIC control method only controls part of the molecules of part of the genetic oscillators, so it has better performance in saving control cost. Moreover, we design an algorithm to obtain sufficient conditions for secure CS and the DoS attacks duration ratio that the system can tolerate. In addition, when the system is immune to DoS attacks, it can still achieve CS under PPIC. Finally, two numerical examples based on MATLAB software are presented to demonstrate the effectiveness of the results. The secure synchronization region is obtained, and the convergence efficiency of error systems under PPIC and pinning impulsive control is compared in the simulation.