Synchronization for the Realization-Dependent Probabilistic Boolean Networks

A Nonaugmented Method for the Minimal Observability of Boolean Networks

This article proposes a nonaugmented method for investigating the minimal observability problem of Boolean networks (BNs). This method can be applied to more general BNs and reduce the computational and space complexity of existing results. First, unobservable states concerning an unobservable BN are classified into three categories using the vertex-colored state transition graph, each accompanied by a necessary and sufficient condition for determining additional measurements to make them distinguishable. Then, an algorithm is designed to identify the additional measurements that would render an unobservable BN observable using the conditions. Next, to determine the minimum added measurements, a necessary and sufficient condition and an algorithm based on a constructed matrix are presented. Finally, the results obtained are compared with existing literature and illustrated with examples.

Long-Run Behavior Estimation of Temporal Boolean Networks With Multiple Data Losses

This brief devotes to investigating the long-run behavior estimation of temporal Boolean networks (TBNs) with multiple data losses, especially the asymptotical stability. The information transmission is modeled by Bernoulli variables, based on which an augmented system is constructed to facilitate the analysis. A theorem guarantees that the asymptotical stability of the original system can be converted to that of the augmented system. Subsequently, one necessary and sufficient condition is obtained for asymptotical stability. Furthermore, an auxiliary system is derived to study the synchronization issue of the ideal TBNs with normal data transmission and TBNs with multiple data losses, as well as an effective criterion for verifying synchronization. Finally, numerical examples are given to illustrate the validity of the theoretical results.

Adaptive Exponential Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay

In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem. In this brief, the AES problem of complex networks with general time-varying delay is addressed, especially when the delay is nondifferentiable. A delay differential inequality is proposed to deal with the exponential stability of delayed nonlinear systems, which is more general than the widely used Halanay inequality. Next, the boundedness of the adaptive control gain is theoretically proved, which is neglected in much of the literature. Then, the AES criteria for networks with general delay are established for the first time by using the proposed inequality and the boundedness of the control gain. Finally, an example is given to demonstrate the effectiveness of the theoretical results.

Perturbation Analysis for Finite-Time Stability and Stabilization of Probabilistic Boolean Networks

This article analyzes the function perturbation impact on the finite-time stability and stabilization of the probabilistic Boolean networks (PBNs). First, the concept of stability in the distribution of PBNs is divided into two disjoint concepts, that is, finite-time stability with probability one (FTSPO) and asymptotical stability with probability one (ASPO), and a new criterion is proposed for the verification of ASPO. Second, by constructing a parameterized set, it is shown that PBNs subject to function perturbation keep FTSPO if and only if the perturbed point does not belong to the parameterized set, while PBNs become ASPO if and only if the perturbed point belongs to the parameterized set. Third, as an application of perturbed stability analysis, the robust state-feedback stabilization is discussed for probabilistic Boolean control networks (PBCNs) with function perturbation. Finally, the obtained results are applied to a WNT5A network and lac operon in the Escherichia coli, respectively.

Robustness and recovery mechanism under the interaction of dependent networks

With the development of society and the progress of science and technology, the process of urban infrastructure construction is accelerating, various infrastructure networks are constantly improving, and the links between different infrastructure networks are getting closer. Compared with a single network, this kind of interdependent network is more complex, and the research results of the existing single network are difficult to explain the nature and phenomenon of this kind of network. This article mainly introduces the research on the robustness and recovery mechanism of interdependent networks. From the perspective of a complex network, this paper combines the interdependence between the networks in the actual system and the node load and builds an interdependent network model. On the basis of the load capacity model, an interdependent network error model is established. And through matlab simulation experiments, the fault propagation characteristics of dependent networks under three conditions and the reliability attack methods of dependent networks are studied. The experimental results in this article show that dependent networks show exceptional vulnerability under deliberate attack functions, while dependent networks show good robustness under random attack modes. In addition, increasing the network node tolerance coefficient can improve the robustness of the interdependent network. When the tolerance is increased from 1 to 10, the robustness of the dependent network is increased by 18%.

A New Method for Topology Identification of Complex Dynamical Networks

Topology identification of complex dynamical networks received extensive attention in the past decade. Most existing studies rely heavily on the linear independence condition (LIC). We find that a critical step in using this condition is not rigorous. Besides, it is difficult to verify this condition. Without regulating the original network, possible identification failure caused by network synchronization cannot be avoided. In this paper, we propose a new method to overcome these shortcomings. We add a regulation mechanism to the original network and construct an auxiliary network consisting of isolated nodes. Along with the outer synchronization between the regulated network and the auxiliary network, we show that the original network can be identified. Our method can avoid identification failure caused by network synchronization. Moreover, we show that there is no need to check the LIC. We finally provide some examples to demonstrate that our method is reliable and has good performances.

Stability and Stabilization in Probability of Probabilistic Boolean Networks

This article studies the stability in probability of probabilistic Boolean networks and stabilization in the probability of probabilistic Boolean control networks. To simulate more realistic cellular systems, the probability of stability/stabilization is not required to be a strict one. In this situation, the target state is indefinite to have a probability of transferring to itself. Thus, it is a challenging extension of the traditional probability-one problem, in which the self-transfer probability of the target state must be one. Some necessary and sufficient conditions are proposed via the semitensor product of matrices. Illustrative examples are also given to show the effectiveness of the derived results.

Asymptotical Feedback Set Stabilization of Probabilistic Boolean Control Networks

In this article, we investigate the asymptotical feedback set stabilization in distribution of probabilistic Boolean control networks (PBCNs). We prove that a PBCN is asymptotically feedback stabilizable to a given subset if and only if (iff) it constitutes asymptotically feedback stabilizable to the largest control-invariant subset (LCIS) contained in this subset. We proposed an algorithm to calculate the LCIS contained in any given subset with the necessary and sufficient condition for asymptotical set stabilizability in terms of obtaining the reachability matrix. In addition, we propose a method to design stabilizing feedback based on a state-space partition. Finally, the results were applied to solve asymptotical feedback output tracking and asymptotical feedback synchronization of PBCNs. Examples were detailed to demonstrate the feasibility of the proposed method and results.

On Optimal Time-Varying Feedback Controllability for Probabilistic Boolean Control Networks

This brief studies controllability for probabilistic Boolean control network (PBCN) with time-varying feedback control laws. The concept of feedback controllability with an arbitrary probability for PBCNs is formulated first, and a control problem to maximize the probability of time-varying feedback controllability is investigated afterward. By introducing semitensor product (STP) technique, an equivalent multistage decision problem is deduced, and then a novel optimization algorithm is proposed to obtain the maximum probability of controllability and the corresponding optimal feedback law simultaneously. The advantages of the time-varying optimal controller obtained by the proposed algorithm, compared to the time-invariant one, are illustrated by numerical simulations.

Optimal State Estimation of Boolean Control Networks With Stochastic Disturbances

This paper presents an investigation of the optimal estimation of state for Boolean control networks subject to stochastic disturbances. The disturbances are modeled as independently and identically distributed processes that are assumed to be both mutually independent and independent of the current and the historical states. An iterative algorithm is proposed to calculate the conditional probability distribution of the state given the output measurements. This algorithm is applied to the problems of minimum mismatching estimation and maximum posterior estimation of the state. An example is provided to illustrate the proposed results.

Local Synchronization of Interconnected Boolean Networks With Stochastic Disturbances

This paper is concerned with the local synchronization problem for the interconnected Boolean networks (BNs) without and with stochastic disturbances. For the case without stochastic disturbances, first, the limit set and the transient period of the interconnected BNs are discussed by resorting to the properties of the reachable set for the global initial states set. Second, in terms of logical submatrices of a certain Boolean vector, a compact algebraic expression is presented for the limit set of the given initial states set. Based on it, several necessary and sufficient conditions are derived assuring the local synchronization of the interconnected BNs. Subsequently, an efficient algorithm is developed to calculate the largest domain of attraction. As for the interconnected BNs with stochastic disturbances, first, mutually independent two-valued random logical variables are introduced to describe the stochastic disturbances. Then, the corresponding local synchronization criteria are also established, and the algorithm to calculate the largest domain of attraction is designed. Finally, numerical examples are employed to illustrate the effectiveness of the obtained results/ algorithms.

Global Pinning Synchronization of Complex Networks With Sampled-Data Communications

This paper investigates the global pinning synchronization problem for a class of complex networks with aperiodic samplings. Combined with the Writinger-based integral inequality, a new less conservative criterion is presented to guarantee the global pinning synchronization of the complex network. Furthermore, a novel condition is proposed under which the complex network is globally pinning synchronized with a given performance index. It is shown that the performance index has a positive correlation with the upper bound of the sampling intervals. Finally, the validity and the advantage of the theoretic results obtained are verified by means of the applications in Chua's circuit and pendulum.