Desynchronization of neuronal firing in multiparameter ultrasound stimulation

Low-intensity transcranial ultrasound stimulation, a novel neuromodulation technique, that possesses the advantages of non-invasiveness, high penetration depth, and high spatial resolution, has achieved positive neuromodulation effects in animal studies. But the regulatory mechanism remains controversial. The intramembrane cavitation effect is considered one of the mechanisms for ultrasound neuromodulation. In this study, the modified equations of ultrasonic cavitation bubble dynamics were coupled with the dual-coupled neuron Hindmarsh-Rose model, small-world neural network model, and the Jansen-Rit neural mass model, which simulate simple coupled neurons, complex neuronal networks, and discharge signals in epileptic disorders respectively. The results demonstrated that ultrasound stimulation has an appreciable modulatory effect on neuronal firing desynchronization in Hindmarsh-Rose model and small-world neural network model. The desynchronization effect is related to the stimulation frequency and intensity. Furthermore, ultrasound stimulation has an inhibitory effect on epileptic seizures, and the effect is enhanced by increasing ultrasound frequency from 0.1-1.0 MHz. This is the first combination of ultrasonic intramembrane cavitation effect theory with neurons and neural network firing desynchronization, which can provide guidance of parametric and theories support for the studies of neurological diseases such as epilepsy and Parkinson's disease.

Synchronization of Complex Dynamical Networks Subject to Noisy Sampling Interval and Packet Loss

This article focuses on the sampled-data synchronization issue for a class of complex dynamical networks (CDNs) subject to noisy sampling intervals and successive packet losses. The sampling intervals are subject to noisy perturbations, and categorical distribution is used to characterize the sampling errors of noisy sampling intervals. By means of the input delay approach, the CDN under consideration is first converted into a delay system with delayed input subject to dual randomness and probability distribution characteristic. To verify the probability distribution characteristic of the delayed input, a novel characterization method is proposed, which is not the same as that of some existing literature. Based on this, a unified framework is then established. By recurring to the techniques of stochastic analysis, a probability-distribution-dependent controller is designed to guarantee the mean-square exponential synchronization of the error dynamical network. Subsequently, a special model is considered where only the lower and upper bounds of delayed input are utilized. Finally, to verify the analysis results and testify the effectiveness and superiority of the designed synchronization algorithm, a numerical example and an example using Chua's circuit are given.

Trajectory Tracking on Uncertain Complex Networks via NN-Based Inverse Optimal Pinning Control

A new approach for trajectory tracking on uncertain complex networks is proposed. To achieve this goal, a neural controller is applied to a small fraction of nodes (pinned ones). Such controller is composed of an on-line identifier based on a recurrent high-order neural network, and an inverse optimal controller to track the desired trajectory; a complete stability analysis is also included. In order to verify the applicability and good performance of the proposed control scheme, a representative example is simulated, which consists of a complex network with each node described by a chaotic Lorenz oscillator.

Full command of a network by a new node: some results and examples

We consider that a network of chaotic identical dynamical systems is connected to a new node. Depending on some properties of the network and on the way that connection is made, the new node may control the network. We consider a full-command connection and analyze the possibility of the network being full-commandable by the new node. For full-commandable networks, we define the full-command-window, a set that includes some of the values that the coupling strength of the new node may assume. We present several results and examples that enlight us how a network can become more vulnerable or resistant to full-command.

A New Model for Complex Dynamical Networks Considering Random Data Loss

Model construction is a very fundamental and important issue in the field of complex dynamical networks. With the state-coupling complex dynamical network model proposed, many kinds of complex dynamical network models were introduced by considering various practical situations. In this paper, aiming at the data loss which may take place in the communication between any pair of directly connected nodes in a complex dynamical network, we propose a new discrete-time complex dynamical network model by constructing an auxiliary observer and choosing the observer states to compensate for the lost states in the coupling term. By employing Lyapunov stability theory and stochastic analysis, a sufficient condition is derived to guarantee the compensation values finally equal to the lost values, namely, the influence of data loss is finally eliminated in the proposed model. Moreover, we generalize the modeling method to output-coupling complex dynamical networks. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed model.

Competitive networks using chaotic circuits with hierarchical structure

Coupled oscillatory systems are good models that are able to describe a variety of higher dimensional nonlinear phenomena. Coupled chaotic circuits produce many kinds of interesting synchronization phenomena. In recent years, research studies on complex networks related to the synchronization of coupled oscillators have attracted much attention. In the real world, there are a variety of different network structures. We focus on the competitive interaction network that includes conflict between two networks. Here, we propose a new paradigm for this competitive interaction network using coupled chaotic circuits.

Compressive-Sensing-Based Structure Identification for Multilayer Networks

The coexistence of multiple types of interactions within social, technological, and biological networks has motivated the study of the multilayer nature of real-world networks. Meanwhile, identifying network structures from dynamical observations is an essential issue pervading over the current research on complex networks. This paper addresses the problem of structure identification for multilayer networks, which is an important topic but involves a challenging inverse problem. To clearly reveal the formalism, the simplest two-layer network model is considered and a new approach to identifying the structure of one layer is proposed. Specifically, if the interested layer is sparsely connected and the node behaviors of the other layer are observable at a few time points, then a theoretical framework is established based on compressive sensing and regularization. Some numerical examples illustrate the effectiveness of the identification scheme, its requirement of a relatively small number of observations, as well as its robustness against small noise. It is noteworthy that the framework can be straightforwardly extended to multilayer networks, thus applicable to a variety of real-world complex systems.

New synchronization criteria for complex delayed dynamical networks with sampled-data feedback control

This paper investigates the synchronization problem for a class of complex delayed dynamical networks (CDDNs) by using sampled-data feedback control. First, an augmented Lyapunov-Krasovskii function (LKF) is constructed, which contains two new triple integral terms to reduce the conservativeness. Second, improved synchronization criteria are proposed by combining reciprocally convex technique with a novel class of integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. Third, the desired sampled-data controllers can be achieved by solving a set of linear matrix inequalities (LMIs). Finally, three numerical simulation examples are presented to demonstrate the effectiveness and advantages of the proposed results.

Simulation of the Dynamics of Bacterial Quorum Sensing

Quorum sensing (QS) is a signaling mechanism that pathogenic bacteria use to communicate and synchronize the production of exofactors to attack their hosts. Understanding and controlling QS is an important step towards a possible solution to the growing problem of antibiotic resistance. QS is a cooperative effort of a bacterial population in which some of the bacteria do not participate. This phenomenon is usually studied using game theory and the non-participating bacteria are modeled as cheaters that exploit the production of common goods (exofactors) by other bacteria. Here, we take a different approach to study the QS dynamics of a growing bacterial population. We model the bacterial population as a growing graph and use spectral graph theory to compute the evolution of its synchronizability. We also treat each bacterium as a source of signaling molecules and use the diffusion equation to compute the signaling molecule distribution. We formulate a cost function based on Lagrangian dynamics that combines the time-like synchronization with the space-like diffusion of signaling molecules. Our results show that the presence of non-participating bacteria improves the homogeneity of the signaling molecule distribution preventing thus an early onset of exofactor production and has a positive effect on the optimization of QS signaling and on attack synchronization.

The architecture of dynamic reservoir in the echo state network

Echo state network (ESN) has recently attracted increasing interests because of its superior capability in modeling nonlinear dynamic systems. In the conventional echo state network model, its dynamic reservoir (DR) has a random and sparse topology, which is far from the real biological neural networks from both structural and functional perspectives. We hereby propose three novel types of echo state networks with new dynamic reservoir topologies based on complex network theory, i.e., with a small-world topology, a scale-free topology, and a mixture of small-world and scale-free topologies, respectively. We then analyze the relationship between the dynamic reservoir structure and its prediction capability. We utilize two commonly used time series to evaluate the prediction performance of the three proposed echo state networks and compare them to the conventional model. We also use independent and identically distributed time series to analyze the short-term memory and prediction precision of these echo state networks. Furthermore, we study the ratio of scale-free topology and the small-world topology in the mixed-topology network, and examine its influence on the performance of the echo state networks. Our simulation results show that the proposed echo state network models have better prediction capabilities, a wider spectral radius, but retain almost the same short-term memory capacity as compared to the conventional echo state network model. We also find that the smaller the ratio of the scale-free topology over the small-world topology, the better the memory capacities.

A general fractional-order dynamical network: synchronization behavior and state tuning

A general fractional-order dynamical network model for synchronization behavior is proposed. Different from previous integer-order dynamical networks, the model is made up of coupled units described by fractional differential equations, where the connections between individual units are nondiffusive and nonlinear. We show that the synchronous behavior of such a network cannot only occur, but also be dramatically different from the behavior of its constituent units. In particular, we find that simple behavior can emerge as synchronized dynamics although the isolated units evolve chaotically. Conversely, individually simple units can display chaotic attractors when the network synchronizes. We also present an easily checked criterion for synchronization depending only on the eigenvalues distribution of a decomposition matrix and the fractional orders. The analytic results are complemented with numerical simulations for two networks whose nodes are governed by fractional-order Lorenz dynamics and fractional-order Rössler dynamics, respectively.

Matrix-measure criterion for synchronization in coupled-map networks

We present conditions for the local and global synchronization in coupled-map networks using the matrix measure approach. In contrast to many existing synchronization conditions, the proposed synchronization criteria do not depend on the solution of the synchronous state and give less limitation on the network connections. Numerical simulations of the coupled quadratic maps demonstrate the potentials of our main results.

Clustering in a network of non-identical and mutually interacting agents

Clustering is a phenomenon that may emerge in multi-agent systems through self-organization: groups arise consisting of agents with similar dynamic behaviour. It is observed in fields ranging from the exact sciences to social and life sciences; consider, for example, swarm behaviour of animals or social insects, the dynamics of opinion formation or the synchronization (which corresponds to cluster formation in the phase space) of coupled oscillators modelling brain or heart cells. We consider a clustering model with a general network structure and saturating interaction functions. We derive both necessary and sufficient conditions for clustering behaviour of the model and we investigate the cluster structure for varying coupling strength. Generically, each cluster asymptotically reaches a (relative) equilibrium state. We discuss the relationship of the model to swarming, and we explain how the model equations naturally arise in a system of interconnected water basins. We also indicate how the model applies to opinion formation dynamics.

Firing synchronization and temporal order in noisy neuronal networks

Noise-induced complete synchronization and frequency synchronization in coupled spiking and bursting neurons are studied firstly. The effects of noise and coupling are discussed. It is found that bursting neurons are easier to achieve firing synchronization than spiking ones, which means that bursting activities are more important for information transfer in neuronal networks. Secondly, the effects of noise on firing synchronization in a noisy map neuronal network are presented. Noise-induced synchronization and temporal order are investigated by means of the firing rate function and the order index. Firing synchronization and temporal order of excitatory neurons can be greatly enhanced by subthreshold stimuli with resonance frequency. Finally, it is concluded that random perturbations play an important role in firing activities and temporal order in neuronal networks.

Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks

Real systems are often subject to both noise perturbations and impulsive effects. In this paper, we study the stability and stabilization of systems with both noise perturbations and impulsive effects. In other words, we generalize the impulsive control theory from the deterministic case to the stochastic case. The method is based on extending the comparison method to the stochastic case. The method presented in this paper is general and easy to apply. Theoretical results on both stability in the pth mean and stability with disturbance attenuation are derived. To show the effectiveness of the basic theory, we apply it to the impulsive control and synchronization of chaotic systems with noise perturbations, and to the stability of impulsive stochastic neural networks. Several numerical examples are also presented to verify the theoretical results.

Partial synchronization on a network with different classes of oscillators

Complete and partial synchronization have been largely studied on networks of identical coupled oscillators. However, we study a network in which not all oscillators when uncoupled show the same dynamics and nonetheless the network shows partial synchronization. Our system is composed by four Rössler oscillators diffusively coupled in a ring. Oscillators 1 and 3 are identical, as 2 and 4 are also. In short, the network is said to be composed of different classes of oscillators (in our example, two classes with two oscillators each). Primary synchronization is defined as the case when all oscillators on the same class are identically synchronized, for all classes. Secondary synchronization is related to the other possible cases of partial synchronization. Both are achieved for the system we have chosen, shown by means of direct integration and transverse Lyapunov exponent computation. Furthermore, evidence of riddled basins of attraction is presented.

Global synchronization in lattices of coupled chaotic systems

Based on the concept of matrix measures, we study global stability of synchronization in networks. Our results apply to quite general connectivity topology. In addition, a rigorous lower bound on the coupling strength for global synchronization of all oscillators is also obtained. Moreover, by merely checking the structure of the vector field of the single oscillator, we shall be able to determine if the system is globally synchronized.

Synchronization in time-varying networks: a matrix measure approach

Synchronization in complex networks has attracted lots of interest in various fields. We consider synchronization in time-varying networks, in which the weights of links are time varying. We propose a useful approach--i.e., the matrix measure approach--to derive some analytically sufficient conditions for synchronization in time-varying networks. These conditions are less conservative than many existing synchronization conditions. Theoretical analysis and numerical simulations of different networks verify our main results.

Synchronization in uncertain complex networks

We consider the problem of synchronization in uncertain generic complex networks. For generic complex networks with unknown dynamics of nodes and unknown coupling functions including uniform and nonuniform inner couplings, some simple linear feedback controllers with updated strengths are designed using the well-known LaSalle invariance principle. The state of an uncertain generic complex network can synchronize an arbitrary assigned state of an isolated node of the network. The famous Lorenz system is stimulated as the nodes of the complex networks with different topologies. We found that the star coupled and scale-free networks with nonuniform inner couplings can be in the state of synchronization if only a fraction of nodes are controlled.

Graph operations and synchronization of complex networks

The effects of graph operations on the synchronization of coupled dynamical systems are studied. The operations range from addition or deletion of links to various ways of combining networks and generating larger networks from simpler ones. Methods from graph theory are used to calculate or estimate the eigenvalues of the Laplacian operator, which determine the synchronizability of continuous or discrete time dynamics evolving on the network. Results are applied to explain numerical observations on random, scale-free, and small-world networks. An interesting feature is that, when two networks are combined by adding links between them, the synchronizability of the resulting network may worsen as the synchronizability of the individual networks is improved. Similarly, adding links to a network may worsen its synchronizability, although it decreases the average distance in the graph.