Narrow Results

Using semi-tensor product of matrices, a matrix expression for multivalued logic is proposed, where a logical variable is expressed as a vector, and a logical function is expressed as a multilinear mapping. Under this framework, the dynamics of a multivalued logical network is converted into a standard discrete-time linear system. Analyzing the network transition matrix, easily computable formulas are obtained to show (a) the number of equilibriums; (b) the numbers of cycles of different lengths; (c) transient period, the minimum time for all points to enter the set of attractors, respectively. A method to reconstruct the logical network from its network transition matrix is also presented. This approach can also be used to convert the dynamics of a multivalued control network into a discrete-time bilinear system. Then, the structure and the controllability of multivalued logical control networks are revealed.

The synchronization for two k-valued logical networks of the same dimensions is studied in this paper. First, based on the theory of semi-tensor product of matrices, the master-slave systems (two k-valued logical networks) are converted into discrete-time systems. Second, both open-loop control and feedback control are provided to make the slave network synchronize with the master k-valued logical network. Finally, examples are provided to illustrate the efficiency of the obtained results.

A shockwave signal has the characteristics of short duration and wide dynamic range, so the wireless test system needs to collect it at a continuous high sampling rate, resulting in a short node life cycle and a large amount of redundant data during the test process. Moreover, test data with confidentiality, if it is still recorded and transmitted in plaintext, will challenge information security. Therefore, a compressed and encrypted acquisition framework based on hyperchaotic compressed sensing and semi-tensor is proposed in this paper. Firstly, a new four-dimensional hyperchaotic system is used to generate a compressed sensing measurement matrix to improve the encryption and anti-noise performance. Secondly, for saving memory space and improving computing efficiency, the semi-tensor product is introduced to reduce the dimension of the measurement matrix exponentially. The experimental results show that the proposed framework can realize the compressed and encrypted acquisition of transient signals with small memory space and low computational complexity. And the acquisition results can be directly transmitted to meet the requirements of real-time wireless transmission bandwidth and information security.

With the development of communication technology, modeling and analysis of Petri nets(PN) with network environment have attracted the attention of researchers. This paper investigates the impact of event delay on the modeling and analysis of Petri nets with the help of semi-tensor product(STP). Firstly, Petri nets with fixed-step event delay is expressed by an algebraic form. Subsequently, networked reversibility is proposed for bounded Petri nets with fixed-step event delay, and its necessary and sufficient conditions are given by a matrix condition. Finally, an example is given to verify the validity of the theoretical results.