Graph-theoretic approach to synchronization of fractional-order coupled systems with time-varying delays via periodically intermittent control.

Highlights • Combining Lyapunov method with graph-theoretic approach, periodically intermittent control is applied to synchronizing the FOCSs with time-varying delays for the first time. And two applications are also given. • Nonlinear coupling, time-varying internal delay and time-varying coupling delay are considered into our model, which is more general no matter in theoretical analysis and real applications. • The synchronization criteria depend on the fractional order, control gain, control rate and control period. Abstract This paper deals with synchronization problem of fractional-order coupled systems (FOCSs) with time-varying delays via periodically intermittent control. Here, nonlinear coupling, time-varying internal delay and time-varying coupling delay are considered when modeling, which makes our model more general in comparison with the most existing fractional-order models. It is the first time that periodically intermittent control is applied to synchronizing FOCSs with time-varying delays. Combining Lyapunov method with graph-theoretic approach, some synchronization criteria are obtained. Moreover, the synchronization criteria we derive depend on the fractional order α , control gain, control rate and control period. Besides, the synchronization issues of fractional-order coupled chaotic systems with time-varying delays and fractional-order coupled Hindmarsh–Rose neuron systems with time-varying delays are also investigated as applications of our theoretical results, and relevant sufficient conditions are derived. Finally, numerical simulations with two examples are provided in order to demonstrate the effectiveness of the theoretical results and the feasibility of control strategy. [ABSTRACT FROM AUTHOR]