Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update

Phase synchronization on spatially embedded duplex networks with total cost constraint

Synchronization on multiplex networks has attracted increasing attention in the past few years. We investigate collective behaviors of Kuramoto oscillators on single layer and duplex spacial networks with total cost restriction, which was introduced by Li et al. [Phys. Rev. Lett. 104, 018701 (2010)] and termed as the Li network afterwards. We first explore how the topology of the network influences synchronizability of Kuramoto oscillators on single layer Li networks and find that the closer the Li network is to a regular lattice, the more difficult for it to evolve into synchronization. Then, we investigate synchronizability of duplex Li networks and find that the existence of inter-layer interaction can greatly enhance inter-layer and global synchronizability. When the inter-layer coupling strength is larger than a certain critical value, inter-layer synchronization will always occur. Furthermore, on single layer Li networks, nodes with larger degrees reach global synchronization more easily than those with smaller degrees, while on duplex Li networks, due to inter-layer interaction, this phenomenon becomes much less obvious. The results are important for us to gain insight into collective behaviors of many real-world complex systems which inherently possess multiplex architecture.

Variable structure controller design for Boolean networks

The paper investigates the variable structure control for stabilization of Boolean networks (BNs). The design of variable structure control consists of two steps: determine a switching condition and determine a control law. We first provide a method to choose states from the reaching mode. Using this method, we can guarantee that the number of nodes which should be controlled is minimized. According to the selected states, we determine the switching condition to guarantee that the time of global stabilization in the BN is the shortest. A control law is then determined to ensure that all selected states can enter into the sliding mode, such that any initial state can arrive in the steady-state mode. Some examples are provided to illustrate the theoretical results.

Observability of Boolean multiplex control networks

Boolean multiplex (multilevel) networks (BMNs) are currently receiving considerable attention as theoretical arguments for modeling of biological systems and system level analysis. Studying control-related problems in BMNs may not only provide new views into the intrinsic control in complex biological systems, but also enable us to develop a method for manipulating biological systems using exogenous inputs. In this article, the observability of the Boolean multiplex control networks (BMCNs) are studied. First, the dynamical model and structure of BMCNs with control inputs and outputs are constructed. By using of Semi-Tensor Product (STP) approach, the logical dynamics of BMCNs is converted into an equivalent algebraic representation. Then, the observability of the BMCNs with two different kinds of control inputs is investigated by giving necessary and sufficient conditions. Finally, examples are given to illustrate the efficiency of the obtained theoretical results.

A simplified computational memory model from information processing

This paper is intended to propose a computational model for memory from the view of information processing. The model, called simplified memory information retrieval network (SMIRN), is a bi-modular hierarchical functional memory network by abstracting memory function and simulating memory information processing. At first meta-memory is defined to express the neuron or brain cortices based on the biology and graph theories, and we develop an intra-modular network with the modeling algorithm by mapping the node and edge, and then the bi-modular network is delineated with intra-modular and inter-modular. At last a polynomial retrieval algorithm is introduced. In this paper we simulate the memory phenomena and functions of memorization and strengthening by information processing algorithms. The theoretical analysis and the simulation results show that the model is in accordance with the memory phenomena from information processing view.

Disturbance Decoupling of Singular Boolean Control Networks

This paper investigates the controller designing for disturbance decoupling problem (DDP) of singular Boolean control networks (SBCNs). Using semi-tensor product (STP) of matrices and the Implicit Function Theorem, a SBCN is converted into the standard BCN. Based on the redundant variable separation technique, both state feedback and output feedback controllers are designed to solve the DDP of the SBCN. Sufficient conditions are also given to analyze the invariance of controllers concerning the DDP of the SBCN with function perturbation. Two illustrative examples are presented to support the effectiveness of these obtained results.

Topology Universality and Dissimilarity in a Class of Scale-Free Networks

We study the effect of subtle changes on the evolution in the scale-free (SF) networks. Three extended models are evolved based on competition and inner anti-preferential deletion in growth and preferential attachment processes. By nonlinear and dynamic controlling on randomness and determinacy, three models can self-organize into scale-free networks, and diverse scaling exponents appear. Moreover, the model with more determinacy has more stringent parameter control than randomness, especially in the edge deletion. Our results suggest that the nature of the topology universality and dissimilarity in SF networks may be the subtle changes of randomness and determinacy.

Synchronization Analysis of Master-Slave Probabilistic Boolean Networks

In this paper, we analyze the synchronization problem of master-slave probabilistic Boolean networks (PBNs). The master Boolean network (BN) is a deterministic BN, while the slave BN is determined by a series of possible logical functions with certain probability at each discrete time point. In this paper, we firstly define the synchronization of master-slave PBNs with probability one, and then we investigate synchronization with probability one. By resorting to new approach called semi-tensor product (STP), the master-slave PBNs are expressed in equivalent algebraic forms. Based on the algebraic form, some necessary and sufficient criteria are derived to guarantee synchronization with probability one. Further, we study the synchronization of master-slave PBNs in probability. Synchronization in probability implies that for any initial states, the master BN can be synchronized by the slave BN with certain probability, while synchronization with probability one implies that master BN can be synchronized by the slave BN with probability one. Based on the equivalent algebraic form, some efficient conditions are derived to guarantee synchronization in probability. Finally, several numerical examples are presented to show the effectiveness of the main results.