Inner synchronization of controlled multi-valued logical networks

This paper studies the inner synchronization problem of multi-valued logical networks by introducing an external single node, which is also called the driving node. Firstly, for the case where the synchronized state of all network nodes equals the state of the driving node, the inner synchronization model of the controlled multi-valued logical network is established, and a necessary and sufficient condition is obtained using the semi-tensor product. Secondly, based on the above synchronization model, a more general model of inner synchronization is discussed, where all nodes of the multi-valued logical network synchronize with each other, but not necessarily to the same as state of the driving node; inner synchronization criteria are established through theoretical proof. Finally, two simulation examples are given to verify the validity of the conclusions.