Synchronization Design of Boolean Networks Via the Semi-Tensor Product Method

We provide a general approach for the design of a response Boolean network (BN) to achieve complete synchronization with a given drive BN. The approach is based on the algebraic representation of BNs in terms of the semi-tensor product of matrices. Instead of designing the logical dynamic equations of a response BN directly, we first construct its algebraic representation and then convert the algebraic representation back to the logical form. The results are applied to a three-neuron network in order to illustrate the effectiveness of the proposed approach.