Jia-Bao Liu

Stability and synchronization of memristor-based fractional-order delayed neural networks

Global asymptotic stability and synchronization of a class of fractional-order memristor-based delayed neural networks are investigated. For such problems in integer-order systems, Lyapunov-Krasovskii functional is usually constructed, whereas similar method has not been well developed for fractional-order nonlinear delayed systems. By employing a comparison theorem for a class of fractional-order linear systems with time delay, sufficient condition for global asymptotic stability of fractional memristor-based delayed neural networks is derived. Then, based on linear error feedback control, the synchronization criterion for such neural networks is also presented. Numerical simulations are given to demonstrate the effectiveness of the theoretical results.

Asymptotic Laplacian-energy-like invariant of lattices

Let µ 1 ? µ 2 ? ? ? µ n denote the Laplacian eigenvalues of a graph G with n vertices. The Laplacian-energy-like invariant, denoted by LEL ( G ) = ? i = 1 n - 1 µ i , is a novel topological index. In this paper, we show that the Laplacian-energy-like per vertex of various lattices is independent of the toroidal, cylindrical, and free boundary conditions. Simultaneously, the explicit asymptotic values of the Laplacian-energy-like in these lattices are obtained. Moreover, our approach implies that in general the Laplacian-energy-like per vertex of other lattices is independent of the boundary conditions.

Remaining useful life estimation using an inverse Gaussian degradation model

The use of degradation data to estimate the remaining useful life (RUL) has gained great attention with the widespread use of prognostics and health management on safety critical systems. Accurate RUL estimation can prevent system failure and reduce the running risks since the efficient maintenance service could be scheduled in advance. In this paper, we present a degradation modeling and RUL estimation approach by using available degradation data for a deteriorating system. An inverse Gaussian process with the random effect is firstly used to characterize the degradation process of the system. Expectation maximization algorithm is then adopted to estimate the model parameters, and the random parameters in the degradation model are updated by Bayesian method, which makes the estimated RUL able to be real-time updated in terms of the fresh degradation data. Our proposed method can capture the latest condition of the system by means of updating degradation data continuously, and obtain the explicit expression of RUL distribution. Finally, a numerical example and a practical case study are provided to show that the presented approach can effectively model degradation process for the individual system and obtain better results for RUL estimation.

The resistance distances of electrical networks based on Laplacian generalized inverse

In this paper, the generalized inverse representations for the Laplacian block matrices of graphs G 1 ? G 2 and G 1 ?s G 2 are proposed, based on which the explicit resistance distance can be obtained for the arbitrary two-vertex resistance in the electrical networks. Moreover, some numerical examples are presented, which show the correction and efficiency of the obtained results.

On degree resistance distance of cacti

A graph G is called a cactus if each block of G is either an edge or a cycle. Denote by C a c t ( n ; t ) the set of connected cacti possessing n vertices and t cycles. In a recent paper (Du et?al., 2015), the C a c t ( n ; t ) with minimum degree resistance distance was characterized. We now determine the elements of C a c t ( n ; t ) with second-minimum and third-minimum degree resistance distances. In addition, some mistakes in Du et?al. (2015) are pointed out.

Minimizing Kirchhoff index among graphs with a given vertex bipartiteness

The resistance distance between any two vertices of a graph G is defined as the effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of the resistance distances between all the pairs of vertices in G. The vertex bipartiteness vb of a graph G is the minimum number of vertices whose deletion from G results in a bipartite graph. In this paper, we characterize the graph having the minimum Kf(G) values among graphs with a fixed number n of vertices and fixed vertex bipartiteness, 1 ź v b ź n - 3 .

Applications of Laplacian spectra for n-prism networks

In this paper, the properties of the Laplacian matrices for the n-prism networks are investigated. We calculate the Laplacian spectra of n-prism graphs which are both planar and polyhedral. In particular, we derive the analytical expressions for the product and the sum of the reciprocals of all nonzero Laplacian eigenvalues. Moreover, these results are used to handle various problems that often arise in the study of networks including Kirchhoff index, global mean-first passage time, average path length and the number of spanning trees. These consequences improve and extend the earlier results. HighlightsWe propose the structure of n-prism networks.We calculate the Laplacian spectra of n-prism networks.We deduce expressions for product and sum of reciprocals of all nonzero Laplacian-eigenvalues.Kirchhoff index, GMFPT, average path length and the number of spanning trees are obtained.

Research on Evolutionary Mechanism of Agile Supply Chain Network via Complex Network Theory

The paper establishes the evolutionary mechanism model of agile supply chain network by means of complex network theory which can be used to describe the growth process of the agile supply chain network and analyze the complexity of the agile supply chain network. After introducing the process and the suitability of taking complex network theory into supply chain network research, the paper applies complex network theory into the agile supply chain network research, analyzes the complexity of agile supply chain network, presents the evolutionary mechanism of agile supply chain network based on complex network theory, and uses Matlab to simulate degree distribution, average path length, clustering coefficient, and node betweenness. Simulation results show that the evolution result displays the scale-free property. It lays the foundations of further research on agile supply chain network based on complex network theory.

The Kirchhoff Index of Folded Hypercubes and Some Variant Networks

The -dimensional folded hypercube is an important and attractive variant of the -dimensional hypercube , which is obtained from by adding an edge between any pair of vertices complementary edges. is superior to in many measurements, such as the diameter of which is , about a half of the diameter in terms of . The Kirchhoff index is the sum of resistance distances between all pairs of vertices in . In this paper, we established the relationships between the folded hypercubes networks and its three variant networks , , and on their Kirchhoff index, by deducing the characteristic polynomial of the Laplacian matrix in spectral graph theory. Moreover, the explicit formulae for the Kirchhoff indexes of , , , and were proposed, respectively.

Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs

The hyper-Zagreb index is an important branch in the Zagreb indices family, which is defined as , where is the degree of the vertex in a graph . In this paper, the monotonicity of the hyper-Zagreb index under some graph transformations was studied. Using these nice mathematical properties, the extremal graphs among -vertex trees (acyclic), unicyclic, and bicyclic graphs are determined for hyper-Zagreb index. Furthermore, the sharp upper and lower bounds on the hyper-Zagreb index of these graphs are provided.