Passive synchronization for Markov jump genetic oscillator networks with time-varying delays

• The passive synchronization problem of Markov jump genetic oscillator networks is proposed.
• We model the Markov jump genetic oscillator networks with time-varying delays and external disturbances.
• Sufficient conditions are established to guarantee that the passive synchronization can be achieved.
• A numerical example is provided to show the effectiveness of our theoretical results.

In this paper, the synchronization problem of coupled Markov jump genetic oscillator networks with time-varying delays and external disturbances is investigated. By introducing the drive-response concept, a novel mode-dependent control scheme is proposed, which guarantees that the synchronization can be achieved. By applying the Lyapunov–Krasovskii functional method and stochastic analysis, sufficient conditions are established based on passivity theory in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of our theoretical results.