2,312 publications from this institution
In this paper, a new topological approach for studying a sufficiently long random number sequence is proposed. By segmenting the sequence into groups of digits which represent the node identities while the undirected edges symbolize the adjacency between them, a network is constructed for analysis. In particular, the network constructed from a π sequence is examined in detail and its properties are contrasted with the Erdos–Renyi (ER) random graph model. Based on the observation that there are more nodes with even degrees than the adjacent odd counterparts in the constructed network, a new random graph model named Random Eulerian (RE) model and its extension are finally proposed and analyzed.
This paper is concerned with a class of 2-dimensional spatiotemporal discrete systems (2d spatiotemporal discrete systems), or 2-dimensional and 2-directional discrete systems (2d–2D discrete systems). Some sufficient conditions for this system to be stable and some illustrative examples for this system to be chaotic in the sense of Devaney and of Li–Yorke are derived and discussed.
This article designs an effective consensus control protocol for continuous-time second-order time-delayed multiagent systems in a multiplicative noisy environment, using absolute velocity and relative position measurements. The nonlinear case and double-integrator case are studied, respectively. Due to the time delay and multiplicative noise in such models, the conventional methods for consensus analysis are not applicable. In this article, therefore, a degenerated Lyapunov functional is used to derive the conditions for mean-square consensus and almost-sure consensus, related to the Lipschitz constants of the nonlinear term, time delay, and noise intensity. In particular, for the double-integrator setting, it is shown that the mean-square consensus and the almost-sure consensus can be achieved by choosing appropriate control gains for any given time delay and noise intensity. To show the effectiveness of the proposed control protocol, some numerical simulations are demonstrated.
The dynamic analysis of a continuous-time multi-agent swarm model with nonlinear profiles is investigated in this paper. It is shown that, under mild conditions, all agents in a swarm can reach cohesion within a finite time, where the upper bounds of the cohesion are derived in terms of the parameters of the swarm model. The results are then generalized by considering stochastic noise and switching between nonlinear profiles. Furthermore, swarm models with limited sensing range inducing changing communication topologies and unbounded repulsive interactions between agents are studied by switching system and nonsmooth analysis. Here, the sensing range of each agent is limited and the possibility of collision among nearby agents is high. Finally, simulation results are presented to demonstrate the validity of the theoretical analysis.
Anti-control of chaos, making a non-chaotic system chaotic, has led to the discovery of some new chaotic systems, particularly the continuous-time three-dimensional autonomous Chen's equation with only two quadratic terms. This paper further investigates some basic dynamical properties and various bifurcations of Chen's equation, thereby revealing its different features from some other chaotic models such as the Lorenz system.
Recently Bu and Wang [Bu S, Wang B-H. Chaos, Solitons & Fractals 2004;19(4):919–24] proposed a simple modulation method aiming to improve the security of chaos-based secure communications against return-map-based attacks. Soon this modulation method was independently cryptanalyzed by Chee et al. [Chee CY, Xu D, Bishop SR. Chaos, Solitons & Fractals 2004;21(5):1129–34], Wu et al. [Wu X, Hu H, Zhang B. Chaos, Solitons & Fractals 2004;22(2):367–73], and Álvarez et al. [Álvarez G, Montoya F, Romera M, Pastor G. Chaos, Solitons & Fractals, in press, arXiv:nlin/0406065] via different attacks. As an enhancement to the Bu–Wang method, an improving scheme was suggested by Wu et al. by removing the relationship between the modulating function and the zero-points. The present paper points out that the improved scheme proposed by Wu et al. is still insecure against a new attack. Compared with the existing attacks, the proposed attack is more powerful and can also break the original Bu–Wang scheme. Furthermore, it is pointed out that the security of the modulation-based schemes proposed by Wu et al. is not so satisfactory from a pure cryptographical point of view. The synchronization performance of this class of modulation-based schemes is also discussed.
For three two-component shallow water wave models, from the approach of dynamical systems and the singular traveling wave theory developed in [Li & Chen, 2007], under different parameter conditions, all possible bounded solutions (solitary wave solutions, pseudo-peakons, periodic peakons, as well as smooth periodic wave solutions) are derived. More than 19 explicit exact parametric representations are obtained. Of more interest is that, for the integrable two-component generalization of the Camassa–Holm equation, it is found that its [Formula: see text]-traveling wave system has a family of pseudo-peakon wave solutions. In addition, its [Formula: see text]-traveling wave system has two families of uncountably infinitely many solitary wave solutions. The new results complete a recent study by Dutykh and Ionescu-Kruse [2016].
This paper presents the design and implementation of a new fuzzy proportional-integration plus fuzzy proportional-derivative control scheme, named the fuzzy P 2 ID controller hereafter, for controlling the handlebar of a bicycle robot with time-varyi
Previous studies concerning pinning control of complex-network synchronization have very often demonstrated that in an unweighted symmetrical scale-free network, controlling the high-degree nodes is more efficient than controlling randomly chosen ones; due to the heterogeneity of the node-degree or edge-connection distribution of the scale-free network, small-degree nodes have relatively high probabilities of being chosen at random but their control has less influence on the other nodes through the network. This raises the question of whether or not controlling the high-degree nodes is always better than controlling the small ones in scale-free networks. Our answer to this is yes and no. In this study, we carry out extensive numerical simulations to show that in an unweighted symmetrical Barabasi–Albert scale-free network, when the portion of controlled nodes is relatively large, controlling the small nodes becomes better than controlling the big nodes and controlling randomly chosen nodes has approximately the same effect as controlling the big ones. However, we also show that for normalized weighted scale-free networks, controlling the big nodes is in fact always better than controlling the small ones.
Complex dynamical networks are attracting more and more attention due to their ubiquity in the natural world. This Letter presents several new delay-dependent conditions for a general complex dynamical network model with coupling delays, which guarantee the synchronized states to be asymptotically stable. These conditions are expressed as linear matrix inequalities, readily solvable by available numerical software. Both continuous- and discrete-time networks are taken into consideration. It is shown theoretically that the condition for continuous-time delayed networks developed in this Letter encompasses an established result in the literature as a special case. In addition, similar delay-dependent results are derived for discrete-time delayed networks, for the first time in the literature. The most important feature of the results obtained in this Letter is that they are less conservative, which is illustrated by a numerical example.
In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.
