Cluster synchronization of fractional-order coupled genetic regulatory networks via pinning control

Cell-to-cell interaction and quorum sensing are universal in real life and have an extremely important biological significance. Besides, fractional-order calculus has tremendous advantages in describing the memory of neurons and the inheritance of genes. In this article, the cluster synchronization of fractional-order coupled genetic regulatory networks (GRNs) is explored by applying pinning control technique. First of all, a type of coupled fractional-order models about GRNs is proposed based on the quorum sensing and cluster expression characteristics of genes. Secondly, by designing pinning control strategies and fractional-order inequalities, several sufficient criteria are constructed to reach cluster synchronization. Furthermore, the selection rule of pining nodes is provided to conduct what nodes can be selected to be pinned and how many nodes are pinned to achieve cluster synchronization. In addition, the fractional-order adaptive control strategy is designed to regulate control gains. Several numerical results are provided lastly to confirm the theoretical analysis.