2,312 publications from this institution
In this paper, we investigate the convergence and stability of a neural network model with different time scales, which models the activity of cortical cognitive maps. We provide a theoretic condition for global exponential convergence of the solutions of the network, which is proved weaker than some existing results in the literature. We also introduce time-varying delays with less constraints into the neural network model and derive a general stability condition for the delay network.
In this big data era, more and more social activities are digitized thereby becoming traceable, and thus the studies of social networks attract increasing attention from academia. It is widely believed that social networks play important role in the process of information diffusion. However, the opposite question, i.e., how does information diffusion process rebuild social networks, has been largely ignored. In this paper, we propose a new framework for understanding this reversing effect. Specifically, we first introduce a novel information diffusion model on social networks, by considering two types of individuals, i.e., smart and normal individuals, and two kinds of messages, true and false messages. Since social networks consist of human individuals, who have self-learning ability, in such a way that the trust of an individual to one of its neighbors increases (or decreases) if this individual received a true (or false) message from that neighbor. Based on such a simple self-learning mechanism, we prove that a social network can indeed become smarter, in terms of better distinguishing the true message from the false one. Moreover, we observe the emergence of social stratification based on the new model, i.e., the true messages initially posted by an individual closer to the smart one can be forwarded by more others, which is enhanced by the self-learning mechanism. We also find the crossover advantage, i.e., interconnection between two chain networks can make the related individuals possessing higher social influences, i.e., their messages can be forwarded by relatively more others. We obtained these results theoretically and validated them by simulations, which help better understand the reciprocity between social networks and information diffusion.
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This technical note addresses the synchronized region problem, which is converted to a more convenient matrix stability problem, for complex dynamical networks. For any natural number <formula formulatype="inline"><tex Notation="TeX">$n$</tex> </formula>, the existence of a network with <formula formulatype="inline"> <tex Notation="TeX">$n$</tex></formula> disconnected synchronized regions is theoretically proved and numerically demonstrated. This shows the intrinsic complexity of the network synchronization problem. Convexity characteristic of stability for relevant matrix pencils is further discussed. A smooth Chua's circuit network is finally discussed as an example for illustration. </para>
In this paper, a generalized epidemic model on complex heterogeneous networks is proposed. To give a theoretical explanation for the simulation results established on networks, mathematical analysis of the epidemic dynamics is presented via mean-field approximation. Stabilities of the disease-free equilibrium and the endemic equilibrium are studied. The results explain why the heterogeneous connectivity patterns impact the epidemic threshold and reveal how the host parameters and the underlying network structures determine disease propagation.
This paper reports the finding of an unusual three-dimensional autonomous quadratic Lorenz-like chaotic system which, surprisingly, has two stable node-type of foci as its only equilibria. The new system contains the diffusionless Lorenz system and the Burke–Shaw system, and some others, as special cases. The algebraic form of the new chaotic system is similar to the other Lorenz-type systems, but they are topologically nonequivalent. To further analyze the new system, some dynamical behaviors such as Hopf bifurcation and singularly degenerate heteroclinic and homoclinic orbits, are rigorously proved with simulation verification. Moreover, it is proved that the new system with some specified parameter values has Silnikov-type homoclinic and heteroclinic chaos.
A new circuitry design based on Chua's circuit for generating n-scroll attractors (n = 1, 2, 3, …) is proposed. In this design, the nonlinear resistor in Chua's circuit is constructed via a systematical procedure using basic building blocks. With the proposed construction scheme, the slopes and break points of the v–i characteristic of the circuit can be tuned independently, and chaotic attractors with an even or an odd number of scrolls can be easily generated. Distinct attractors with n-scrolls (n = 5, 6, 7, 8, 9, 10) obtained with this simple experimental set-up are demonstrated.
Based on the asymptotic stability theory of dynamical systems and matrix theory, a general criterion of synchronization stability of N coupled neurons with symmetric configurations is established in this Letter. Especially, three types of connection styles (that is, chain, ring and global connections) are considered. As an illustration, complete synchronization of four coupled identical chaotic Chay neurons is investigated. The maximal conditional Lyapunov exponent is calculated and used to determine complete synchronization. As a result, complete synchronization of four coupled identical chaotic Chay neurons can be achieved when the coupling strength is above a critical value, which is dependent on the specific connection style. Numerical simulation is in good agreement with the theoretical analysis.
This paper studies robust impulsive synchronization of uncertain dynamical networks. By utilizing the concept of im- pulsive control and the stability results for impulsive systems, sev- eral criteria for robust local and robust global impulsive synchro- nization are established for complex dynamical networks, in which the network coupling functions are unknown but bounded. Three examples are also worked through for illustrating the main results. Index Terms—Chaotic synchronization, globally robustly impul- sive synchronization, locally robust impulsive synchronization, net- work coupling, uncertain dynamical networks.
Fuzzy control systems are developed based on fuzzy set theory, attributed to Lotfi A. Zadeh (Zadeh, 1965, 1973), which extends the classical set theory with memberships of its elements described by the classical characteristic function (either “is” or “is not” a member of the set), to allow for partial membership described by a membership function (both “is” and “is not” a member of the set at the same time, with a certain degree of belonging to the set). Thus, fuzzy set theory has great capabilities and flexibilities in solving many real-world problems which classical set theory does not intend or fails to handle. Fuzzy set theory was applied to control systems theory and engineering almost immediately after its birth. Advances in modern computer technology continuously backs up the fuzzy framework for coping with engineering systems of a broad spectrum, including many control systems that are too complex or too imprecise to tackle by conventional control theories and techniques
Bifurcation control means modifying some essential bifurcation characteristics of a parameterized system by designing a controller. It has evoked wide attention and interest due to its mathematical analysis and engineering applications. In the real world, the appearance of bifurcation in a physical, biological, or electric power system is non-beneficial or even dangerous, so it should be suppressed. In this paper, as an efficient bifurcation control technique, we propose a simple but effective methodology for suppression of bifurcation of continuous dynamical systems.
This brief reviews the millennium transition of the IEEE Circuits and Systems Society Newsletter to Magazine.
Over the last decade, complex networks have been intensively studied across many fields, especially in Internet technology, biological engineering, and nonlinear science. This paper will briefly review the main advances in the investigation of complex networks, with emphasis on the recent progress of complex networks in control and synchronization.
This Letter contains three parts. First, it analyzes some basic properties of a new complex four-dimensional (4D) continuous autonomous chaotic system, in which each equation contains a cubic cross-product term. The new system has 9 equilibria, which display graceful symmetry with respect to the origin and the coordinate planes, and they have similarity associated with their linearized characteristics and along with invariant manifolds. Second, under constant control, the system displays (i) two coexisting symmetric double-wing chaotic attractors simultaneously, and (ii) two coexisting asymmetric double-wing and two coexisting single-wing attractors including chaotic, period-doubling, and periodic orbits. The evolution process of an attractor from double-wing to single-wing is investigated via a distribution diagram of equilibria and bifurcation diagrams of the system states. Finally, several circuits are built for different configurations of the new system, which show a good agreement between computer simulations and experimental results, revealing some important distinctions in applications arising from different frequencies used.
The cyclicity of period annuli of some classes of reversible andnon-Hamiltonian quadratic systems under quadratic perturbationsare studied. The argument principle method and the centroid curvemethod are combined to prove that the related Abelian integral hasat most two zeros.
No abstract is provided for this article.
