This paper focuses on the neurodynamical research of a small neural network that consists of 25 neurons. We study the periodic spontaneous activity and transitions between up and down states without synaptic input. The results demonstrate that these transitions are bidirectional or unidirectional with the parameters changing, which not only reveals the function of the cortex, but also cohere with the experiment results.

This paper is concerned with the study of entrained collective rhythms of multicellular systems by using partial impulsive control strategy. The objective is to design an impulsive controller based on only those partially available cell states, so that the entrained collective rhythms are guaranteed for the multicellular systems with cell-to-cell communication mechanism. By using the newly developed impulsive integrodifferential inequality, the sufficient conditions are derived to achieve the entrained collective rhythms of multicellular systems. A synthetic multicellular system with simulation results is finally given to illustrate the usefulness of the developed results.

Small-world networks are ubiquitous in real-life systems, such as the World Wide Web, communication networks, and electric power grids, and most of them are stochastic. In this paper, we present a model that generates a small-world network in a simple deterministic way and analyze the relevant topological properties of the model, such as the degree distribution, clustering coefficient, and diameter. Meanwhile, according to the special structure of the model, we derive analytically the exact numbers of spanning trees in the planar networks. The results show that the model has a discrete exponential degree distribution, high clustering coefficient, short diameter, and high entropy.

A new function projective synchronization scheme between different fractional-order chaotic systems, called scaling-base drive function projective synchronization (SBDFPS), is discussed. In this SBDFPS scheme, one fractional-order chaotic system is chosen as scaling drive system, one fractional-order chaotic system is chosen as base drive systems, and another fractional-order chaotic system is chosen as response system. The SBDFPS technique scheme is based on the stability theory of nonlinear fractional-order systems, and the synchronization technique is theoretically rigorous. Numerical experiments are presented and show the effectiveness of the SBDFPS scheme.

We study opinion dynamics in social networks and present a new strategy to control the invasive opinion. A developed continuous-opinion evolution model is proposed to describe the mechanism of making decision in closed community. Two basic strategies of evolution are determined, and some basic features of our new model are analyzed. We study the different invasive strategies. It is shown via using Monte Carlo simulations that our new model shows different invulnerability with traditional model. Node degree and cohesion in invasive small-world community plays less significant role when the evolution of opinion is continuous rather than dichotomous. Using simulation, we find one kind of Influential Nodes that can affect the outcome dramatically, while these Influential Nodes are sensitive to their node degree and the evolution weight. Thus, we develop invasive control strategy based on these features.

Bacterial quorum sensing (QS) is an important process of cell communication and more and more attention is paid to it. Moreover, the noises are ubiquitous in nature and often play positive role. In this paper, we investigate how the noise enhances the QS though the stochastic resonance (SR) and explain the mechanism of SR in this quorum sensing network. In addition, we also discuss the interaction between the small RNA and the other genes in this network and discover the biological importance.

This paper investigates the synchronization problem for neural networks with leakage delay and both discrete and distributed time-varying delays under sampled-data control. By employing the Lyapunov functional method and using the matrix inequality techniques, a delay-dependent LMIs criterion is given to ensure that the master systems and the slave systems are synchronous. An example with simulations is given to show the effectiveness of the proposed criterion.

We investigate synchronization between two discrete-time networks with mutual couplings, including inner synchronization inside each network and outer synchronization between two networks. We then obtain a synchronized criterion for the inner synchronization inside each network by the method of linear matrix inequality and derive a relationship between the inner and outer synchronization. Finally, we show numerical examples to verify our theoretical analysis and discuss the effect of coupling strengths, node dynamics, and topological structures on the inner and outer synchronization. Compared to the inner synchronization inside each network, the outer synchronization between two networks is difficult to achieve.

The problem of projective lag synchronization of coupled neural networks with time delay is investigated. By means of the Lyapunov stability theory, an intermittent controller is designed for achieving projective lag synchronization between two delayed neural networks systems. Numerical simulations on coupled Lu neural systems illustrate the effectiveness of the results.

Combined heat and power dynamic economic emission dispatch (CHPDEED) problem is a complicated nonlinear constrained multiobjective optimization problem with nonconvex characteristics. CHPDEED determines the optimal heat and power schedule of committed generating units by minimizing both fuel cost and emission simultaneously under ramp rate constraints and other constraints. This paper proposes hybrid differential evolution (DE) and sequential quadratic programming (SQP) to solve the CHPDEED problem with nonsmooth and nonconvex cost function due to valve point effects. DE is used as a global optimizer, and SQP is used as a fine tuning to determine the optimal solution at the final. The proposed hybrid DE-SQP method has been tested and compared to demonstrate its effectiveness.

Synchronization of complex networks has been extensively studied in many fields, where intensive efforts have been devoted to the understanding of its mechanisms. As for discriminating network synchronizability by Master Stability Function method, a dilemma usually encountered is that we have no prior knowledge of the network type that the synchronous region belongs to. In this paper, we investigate a sufficient condition for a general complex dynamical network in the absence of control. A main result is that, when the coupling strength is sufficiently strong, the dynamical network achieves synchronization provided that the symmetric part of the inner-coupling matrix is positive definite. According to our results, synchronous region of the network with positive definite inner-coupling matrix belongs to the unbounded one, and then the eigenvalue of the outer-coupling matrix nearest 0 can be used for judging synchronizability. Even though we cannot gain the necessary and sufficient conditions for synchronizing a network so far, our results constitute a first step toward a better understanding of network synchronization.

The state estimation problem is investigated for neural networks with leakage delay and time-varying delay as well as for general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing matrix inequality techniques, a delay-dependent linear matrix inequalities (LMIs) condition is developed to estimate the neuron state with some observed output measurements such that the error-state system is globally asymptotically stable. An example is given to show the effectiveness of the proposed criterion.

The passivity and passification for Takagi-Sugeno (T-S) fuzzy systems with leakage delay and both discrete and distributed time-varying delays are investigated. By employing the Lyapunov functional method and using the matrix inequality techniques, several delay-dependent criteria to ensure the passivity and passification of the considered T-S fuzzy systems are established in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. The obtained results generalize some previous results. Two examples are given to show the effectiveness of the proposed criteria.

A novel approach is brought forward for synchronization of a clustered network in this paper, the objective of which is twofold. The first one is to study cluster synchronization by analyzing the inner coupling matrices of the individual clusters instead of the one of the whole network. The other is to show that full synchronization can be ensured by several types of cluster synchronization, the partitions of which are connected together. Compared with the classical method for full synchronization, our approach reduces the network size to the cluster size and additionally obtains the thresholds for different types of cluster synchronization. As a numerical example, cluster and full synchronization in a special clustered network are investigated through our approach. It turns out that we obtain the same threshold for full synchronization as the one obtained by the classical method. Numerical simulations confirm the validity of our approach.

This paper considers the complete synchronization problem for $N$ coupled chaotic systems with ring connections. First, we use a direct design method to design a synchronization controller. It transforms the error system into a stable system with special antisymmetric structure. And then, we get some simple stability criteria of achieving the complete synchronization. These criteria are not only easily verified but also improve and generalize previous known results. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical analysis.

We provide a new gossip algorithm to investigate the problem of opinion consensus with the time-varying influence factors and weakly connected graph among multiple agents. What is more, we discuss not only the effect of the time-varying factors and the randomized topological structure but also the spread of misinformation and communication constrains described by probabilistic quantized communication in the social network. Under the underlying weakly connected graph, we first denote that all opinion states converge to a stochastic consensus almost surely; that is, our algorithm indeed achieves the consensus with probability one. Furthermore, our results show that the mean of all the opinion states converges to the average of the initial states when time-varying influence factors satisfy some conditions. Finally, we give a result about the square mean error between the dynamic opinion states and the benchmark without quantized communication.

This paper proposes two Cucker-Smale-type flocking models by introducing both cohesive and repulsive forces to second-order multiagent systems. Under some mild conditions on the initial state of the flocking system, it is shown that the velocity consensus of the agents can be reached independent of the parameter which describes the decay of communication rates. In particular, the collision between any two agents can always be avoided by designing an appropriate bounded repulsive function based on the initial energy of the flock. Numerical examples are given to demonstrate the effectiveness of the theoretical analysis.

This paper is concerned with the consensus problem of general linear discrete-time multiagent systems (MASs) with random packet dropout that happens during information exchange between agents. The packet dropout phenomenon is characterized as being a Bernoulli random process. A distributed consensus protocol with weighted graph is proposed to address the packet dropout phenomenon. Through introducing a new disagreement vector, a new framework is established to solve the consensus problem. Based on the control theory, the perturbation argument, and the matrix theory, the necessary and sufficient condition for MASs to reach mean-square consensus is derived in terms of stability of an array of low-dimensional matrices. Moreover, mean-square consensusable conditions with regard to network topology and agent dynamic structure are also provided. Finally, the effectiveness of the theoretical results is demonstrated through an illustrative example.

Many facts indicate that the impulsive control method is a finer method, which is simple, efficient, and low in cost, for achieving consensus. In this paper, based on graph theory, Lyapunov stability theory, and matrix theory, a novel impulsive control protocol is given to realize the consensus of the multiagent network. Numerical simulations are performed to verify the theoretical results.

A criterion for the uniform asymptotic stability of the equilibrium point of impulsive delayed Hopfield neural networks is presented by using Lyapunov functions and linear matrix inequality approach. The criterion is a less restrictive version of a recent result. By means of constructing the extended impulsive Halanay inequality, we also analyze the exponential stability of impulsive delayed Hopfield neural networks. Some new sufficient conditions ensuring exponential stability of the equilibrium point of impulsive delayed Hopfield neural networks are obtained. An example showing the effectiveness of the present criterion is given.

This paper proposed a crime busting model with two dynamic ranking algorithms to detect the likelihood of a suspect and the possibility of a leader in a complex social network. Signally, in order to obtain the priority list of suspects, an advanced network mining approach with a dynamic cumulative nominating algorithm is adopted to rapidly reduce computational expensiveness than most other topology-based approaches. Our method can also greatly increase the accuracy of solution with the enhancement of semantic learning filtering at the same time. Moreover, another dynamic algorithm of node contraction is also presented to help identify the leader among conspirators. Test results are given to verify the theoretical results, which show the great performance for either small or large datasets.