Restabilization of perturbed Boolean control networks based on absorbable attractors

The paper studies the restabilization problem of Boolean control networks (BCNs) under the function perturbation. First, an important concept-absorbable attractor is proposed for BCNs. Then, by using this concept, a necessary and sufficient restabilizability criterion is established. This criterion can be used to check whether the perturbed BCN can be restabilized to its original state by modifying the minimum number of parameters in the old controller. Finally, a constructive fine-tuning method is given to modify the old controller. Compared with the existing results, which can only solve the problem of single column function perturbation, our results are more powerful since they are applicable not only to the single column function perturbation problem but also to the case of multiple columns. Finally, two examples are employed to show the effectiveness of our results.