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This paper investigates the stabilization of probabilistic Boolean networks(PBNs) via a novel pinning control strategy based on network structure. In aPBN, the evolution equation of each gene switches among a collection ofcandidate Boolean functions with probability distributions that govern theactivation frequency of each Boolean function. Owing to the stochasticity, theuniform state feedback controller, independent of switching signal, might beout of work, and in this case, the non-uniform state feedback controller isrequired. Subsequently, a criterion is derived to determine whether uniformcontrollers is applicable to achieve stabilization. It is worth pointing outthat the pinning control designed in this paper is based on the networkstructure, which only requires local in-neighbors' information, rather thanglobal information (state transition matrix). Moreover, this pinning controlstrategy reduces the computational complexity from $O(2^{2n})$ to$O(n2^\alpha)$, and thus it has the ability to handle some large-scalenetworks, especially the networks with sparse connections. Finally, themammalian cell-cycle encountering a mutated phenotype is modelled by a PBN todemonstrate the obtained results.

Pinning Stabilizer Design for Large-Scale Probabilistic Boolean Networks