Publications

Data-Driven Cooperative Output Regulation of Continuous-Time Multi-Agent Systems with Unknown Network Topology

This paper investigates data-driven cooperative output regulation for continuous-time multi-agent systems with unknown network topology. Unlike existing studies that typically assume a known network topology to directly compute controller parameters, a novel approach is proposed that allows for the computation of the parameter without prior knowledge of the topology. A lower bound on the minimum non-zero eigenvalue of the Laplacian matrix is estimated using only edge weight bounds, enabling the output regulation controller design to be independent of global network information. Additionally, the common need for state derivative measurements is eliminated, reducing the amount of data requirements. Furthermore, necessary and sufficient conditions are established to ensure that the data are informative for cooperative output regulation, leading to the design of a distributed output regulation controller. For the case with noisy data, the bound of the output error is provided, which is positively correlated with the noise bound, and a distributed controller is constructed for the approximate cooperative output regulation. Finally, the effectiveness of the proposed methods is verified through numerical simulations.

Naming Game with Multi-Hearers or Group Discussions

No abstract is provided for this article.

Synchronization transition in gap-junction-coupled leech neurons

Real neurons can exhibit various types of firings including tonic spiking, bursting as well as silent state, which are frequently observed in neuronal electrophysiological experiments. More interestingly, it is found that neurons can demonstrate the co-existing mode of stable tonic spiking and bursting, which depends on initial conditions. In this paper, synchronization in gap-junction-coupled neurons with co-existing attractors of spiking and bursting firings is investigated as the coupling strength gets increased. Synchronization transitions can be identified by means of the bifurcation diagram and the correlation coefficient. It is illustrated that the coupled neurons can exhibit different types of synchronization transitions between spiking and bursting when the coupling strength increases. In the course of synchronization transitions, an intermittent synchronization can be observed. These results may be instructive to understand synchronization transitions in neuronal systems.

INTRODUCTION TO COMPLEX NETWORKS AND THEIR RECENT ADVANCES

This article introduces the new notion of complex networks,especially the representative models of random-graph networks,small-world networks and scale-free networks as well as related basic concepts and modeling parameters.It also briefly summarizes their applications to biological systems and neural networks, epidemic spreading and immunization over networks,transportation systems,social and economic networks, wireless communication and sensor networks.And finally it reviews the problems of distributed control,stability and consensus analysis in their applications to swarming,flocking and synchronization.

Experimental verification of multidirectional multiscroll chaotic attractors

A systematic methodology for circuit design is proposed for experimental verification of multidirectional multiscroll chaotic attractors, including one-directional (1-D) n-scroll, 2-D n/spl times/m-grid scroll, and 3-D n/spl times/m/spl times/l-grid scroll chaotic attractors. Two typical cases are investigated in detail: the hysteresis and saturated multiscroll chaotic attractors. A simple blocking circuit diagram is designed for experimentally verifying 1-D 5/spl sim/11-scroll, 2-D 3/spl times/5/spl sim/11-grid scroll, and 3-D 3/spl times/3/spl times/5/spl sim/11-grid scroll hysteresis chaotic attractors by manipulating the switchers. Moreover, a block circuitry is also designed for physically realizing 1-D 10, 12, 14-scroll, 2-D 10, 12, 14/spl times/10-grid scroll, and 3-D 10/spl times/10/spl times/10-grid scroll saturated chaotic attractors via switching. In addition, one can easily realize chaotic attractors with a desired odd number of scrolls by slightly modifying the corresponding voltage saturated function series of the circuit, to produce for instance a 1-D 13-scroll saturated chaotic attractor. This is the first time in the literature to report an experimental verification of a 1-D 14-scroll, a 2-D 14/spl times/10-grid scroll and a 3-D 10/spl times/10/spl times/10-grid (totally 1000) scroll chaotic attractors. Only the 3-D case is reported in detail for simplicity of presentation. It is well known that hardware implementation of 1-D n-scroll with n/spl ges/10, 2-D n/spl times/m-grid scroll with n,m/spl ges/10, and 3-D n/spl times/m/spl times/l-grid scroll with n,m,l/spl ges/10 chaotic attractors is very difficult technically, signifying the novelty and significance of the achievements reported in this paper. Finally, this circuit design approach provides some principles and guidelines for hardware implementation of chaotic attractors with a multidirectional orientation and with a large number of scrolls, useful for future circuitry design and engineering applications.

On equilibria, stability, and instability of Hopfield neural networks

Existence and uniqueness of equilibrium, as well as its stability and instability, of a continuous-time Hopfield neural network are studied. A set of new and simple sufficient conditions are derived.

Bifurcations and Dynamics of Traveling Wave Solutions for the Regularized Saint-Venant Equation

This paper studies the bifurcations of phase portraits for the regularized Saint-Venant equation (a two-component system), which appears in shallow water theory, by using the theory of dynamical systems and singular traveling wave techniques developed in [Li & Chen, 2007] under different parameter conditions in the two-parameter space. Some explicit exact parametric representations of the solitary wave solutions, smooth periodic wave solutions, periodic peakons, as well as peakon solutions, are obtained. More interestingly, it is found that the so-called [Formula: see text]-traveling wave system has a family of pseudo-peakon wave solutions, and their limiting solution is a peakon solution. In addition, it is found that the [Formula: see text]-traveling wave system has two families of uncountably infinitely many solitary wave solutions and compacton solutions.

Extending the Symbolic Dynamics of Chua's Bernoulli-Shift Rule 56.

No abstract is provided for this article.

Decoupling of Filtering Equations

No abstract is provided for this article.

Controlling bifurcations of discrete maps

Decoupling process for better synchronizability on scale-free networks

We propose a decoupling process performed in scale-free networks to enhance the synchronizability of the network, together with preserving the scale-free structure. Simulation results show that the decoupling process can effectively promote the network synchronizability, which is measured in terms of eigenratio of the coupling matrix. Moreover, we investigate the correlation between some important structural properties and the collective synchronization, and find that the maximum vertex betweenness seems to be the most strongly correlated with the synchronizability among the major structural features considered. We explain the effect of the decoupling process from a viewpoint of coupling information transmission. Our work provides some evidence that the dynamics of synchronization is related to that of information or vehicle traffic. Because of the low cost in modifying the coupling network, the decoupling process may have potential applications.

BIFURCATION FROM AN EQUILIBRIUM OF THE STEADY STATE KURAMOTO–SIVASHINSKY EQUATION IN TWO SPATIAL DIMENSIONS

The paper deals with the steady state bifurcations of the Kuramoto–Sivashinsky (K–S) equation in two spatial dimensions with zero mean and periodic boundary value conditions. Applying the perturbation method, asymptotic expressions of the steady state solution branches that have bifurcated from the equilibrium are obtained. Furthermore, stability of the bifurcated solution branches is discussed.

A CHAOTIC SYSTEM WITH ONE SADDLE AND TWO STABLE NODE-FOCI

This paper reports the finding of a chaotic system with one saddle and two stable node-foci in a simple three-dimensional (3D) autonomous system. The system connects the original Lorenz system and the original Chen system and represents a transition from one to the other. The algebraical form of the chaotic attractor is very similar to the Lorenz-type systems but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact that the chaotic system has a chaotic attractor, one saddle and two stable node-foci. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations.

Answering two open problems on Banks theorem for non-autonomous dynamical systems

This paper shows that (1) there exists a topologically transitive NADS having two disjoint invariant periodic orbits with dense periodic points, which is finitely generated but not periodic; (2) there exists a topologically transitive non-finitely generated NADS having two disjoint invariant periodic orbits with dense periodic point, which is not sensitive. This answers positively the Open Problems 4.1 and 4.2 posed in [8].

From Chaos to Order

No abstract is provided for this article.

Supervised Learning via Modified Extended Kalman Filtering

No abstract is provided for this article.

Consensus of multi-agent systems with Lipschitz nonlinear dynamics and intermittent communications

Multiple dynamical agents may communicate with their neighbors only during some discontinuous time intervals in real environments. Motivated by this observation, distributed consensus problem is investigated in this paper for a class of multiagent systems with discontinuous communications, where each agent has intrinsic higher-order Lipschitz nonlinear dynamics. Under the assumption that the communication topology is strongly connected, a new class of distributed control algorithms based merely on the intermittent relative states of neighboring agents are constructed. By using tools from switched systems theory, it is shown that consensus in the closed-loop multi-agent systems can be achieved asymptotically if the general algebraic connectivity of the fixed topology is larger than a threshold value. The effectiveness of the analytical results is verified by numerical simulations.

Synchronization of general discrete Lur’e systems

No abstract is provided for this article.