Volume 8 (2018): Issue 4 (October 2018)

A topological index is a numeric quantity associated with a network or a graph that characterizes its whole structural properties. In [Javaid and Cao, Neural Computing and Applications, DOI 10.1007/s00521-017-2972-1], the various degree-based topological indices for the probabilistic neural networks are studied. We extend this study by considering the calculations of the other topological indices, and derive the analytical closed formulas for these new topological indices of the probabilistic neural network. Moreover, a comparative study using computer-based graphs has been carried out first time to clarify the nature of the computed topological descriptors for the probabilistic neural networks. Our results extend some known conclusions.

This paper investigates the global exponential synchronization and quasi-synchronization of inertial memristive neural networks with time-varying delays. By using a variable transmission, the original second-order system can be transformed into first-order differential system. Then, two types of drive-response systems of inertial memristive neural networks are studied, one is the system with parameter mismatch, the other is the system with matched parameters. By constructing Lyapunov functional and designing feedback controllers, several sufficient conditions are derived respectively for the synchronization of these two types of drive-response systems. Finally, corresponding simulation results are given to show the effectiveness of the proposed method derived in this paper.

In this paper, a continuous-time distributed algorithm is presented to solve a class of decomposable quadratic programming problems. In the quadratic programming, even if the objective function is nonconvex, the algorithm can still perform well under an extra condition combining with the objective, constraint and coupling matrices. Inspired by recent advances in distributed optimization, the proposed continuous-time algorithm described by multi-agent network with consensus is designed and analyzed. In the network, each agent only accesses the local information of its own and from its neighbors, then all the agents in a connected network cooperatively find the optimal solution with consensus.

This paper is concerned with cluster consensus of linear multi-agent systems via a distributed event-triggered control scheme. Assume that agents can be split into several clusters and a leader is associated with each cluster. Sufficient conditions are derived to guarantee the realization of cluster consensus by a feasible event-triggered controller if the network topology of each cluster has a directed spanning tree and the couplings within each cluster are sufficiently strong. Further, positive inner-event time intervals are ensured for the proposed event-triggered strategy to avoid Zeno behaviors. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

The adjacency matrix of a graph is a matrix which represents adjacent relation between the vertices of the graph. Its minimum eigenvalue is defined as the least eigenvalue of the graph. Let G_n be the set of the graphs of order n, whose complements are connected and have pendent paths. This paper investigates the least eigenvalue of the graphs and characterizes the unique graph which has the minimum least eigenvalue in G_n.