2,312 publications from this institution
We investigate synchronization in a network of continuous-time dynamical systems with small-world connections. The small-world network is obtained by randomly adding a small fraction of connection in an originally nearest-neighbor coupled network. We show that, for any given coupling strength and a sufficiently large number of cells, the small-world dynamical network will synchronize, even if the original nearest-neighbor coupled network cannot achieve synchronization under the same condition.
In this paper, synchronization of a network coupled with complex-variable chaotic systems is investigated. Adaptive feedback control and intermittent control schemes are adopted for achieving adaptive synchronization and exponential synchronization, respectively. Several synchronization criteria are established. In these schemes, the outer coupling matrix is not necessarily assumed to be symmetric or irreducible. Further, for a class of networks with an irreducible and balanced outer coupling matrix, a pinning control scheme is adopted for achieving synchronization. Numerical simulations are demonstrated to verify the effectiveness of the theoretical results.
A functional version of LaSalle's invariance principle is derived, i.e., rather than the usual pointwise Lyapunov-like functions it uses specially constructed functionals along system trajectories. This modification enables the principle to handle even nonautonomous systems to which the classical LaSalle's principle is not directly applicable. The new theoretical results are then used to study robust synchronization of general Lie/spl acute/nard type of systems. The developed technique is finally applied to chaotic oscillators synchronization. Numerical simulation is included to demonstrate the effectiveness of the proposed methodology.
Based on the Lyapunov stabilization theory and Gerschgorin theorem, a simple generic criterion is derived for global synchronization of two coupled chaotic systems with a unidirectional linear error feedback coupling. This simple criterion is applicable to a large class of chaotic systems, where only a few algebraic inequalities are involved. To demonstrate the efficiency of design, the suggested approach is applied to some typical chaotic systems with different types of nonlinearities, such as the original Chua’s circuit, the modified Chua’s circuit with a sine function, and the Rössler chaotic system. It is proved that these synchronizations are ensured by suitably designing the coupling parameters.
Part 1 Prologue - chaos and order ordering chaos organization of the monograph. Part 2 Parametric variation approaches: parametric variation for control of chaos an earlier attempt the OGY method and its variants new development. Part 3 Conventional engineering control approaches: engineering perspectives on control of chaos controlling chaos via external forces open-loop control methods feedback mechanism - a control engineer's perspective controlling discrete-time chaotic systems controlling continuous-time chaotic systems a closer look at Lyapunov-type approach adaptive control of chaotic systems optimal control of chaotic systems robust control of chaotic systems a stochastic control technique new development. Part 4 Other approaches to controlling chaos: intelligent control approaches controlling chaos in DAI systems synchronization and control of chaos unification of synchronization and control new development. Part 5 Some applications of controlling chaos: chaotic synchronization for secure communication chaos and biomedical systems chaos and biochemical systems controlling chaos of laser systems controlling chaos in fluid dynamics new development. Part 6 Controlling chaos - further discussions: general perspectives to probe further toward an integrated and unified framework.
Most existing flocking algorithms rely on information about both relative position and relative velocity among neighbouring agents. In this article, we investigate the flocking problem with only position measurements. We propose a provably-stable flocking algorithm, in which an output vector is produced by distributed filters based on position information alone but not velocity information. Under the assumption that the initial interactive network is connected, the flocking algorithm not only can steer a group of agents to a stable flocking motion, but also can preserve the connectivity of the interactive network during the dynamical evolution. Moreover, we investigate the flocking algorithm with a virtual leader and show that all agents can asymptotically attain a desired velocity even if only one agent in the team has access to the information of the virtual leader. We finally show some numerical simulations to illustrate the theoretical results.
A highlight of the chaotic spiking backpropagation (CSBP) method, which is a powerful tool for directly training spiking neural networks and helps to understand the learning mechanisms of human brain.
This paper shows that the maximum synchronizability of a general time-invariant dynamical network is completely determined by its associated internal feedback dynamics, which has a precise physical meaning in terms of synchronous communication. Also, a concept of synchronizability matrix is introduced to characterize the robustness of synchronization of the network. Based on the knowledge of synchronizability, we can purposefully increase the robustness of the network synchronization and better prevent it from attacks.
S-type locally-active memristor (LAM) has a great potential for brain- inspired neuromorphic computing, where the S-type LAM-based oscillator is a fundamental building block. Concerning the S-type LAM, this paper constructs a material-independent model in simple mathematical expression, which can be relatively easily analyzed. By biasing the memristor into the locally- active region, and connecting it with a capacitor, a second-order oscillator can be built. The small-signal equivalent circuit of the memristor and its frequency response are applied to determine the period oscillation frequency range and compensation capacitance. Hopf bifurcation theory is used to analyze oscillation mechanism of the second-order circuit and appropriate capacitance. By adding an extra inductor into the second-order oscillator, a novel third-order chaotic circuit is developed, where a saddle-focus is derived to create chaos. Its dynamic characteristics are investigated via Lyapunov exponents, bifurcation diagrams, dynamic route map, and so on. The local activities of the single memristor, second-order oscillator, and third-order chaotic circuit are verified through the mathematical analysis. Finally, physical circuit realizations of the S- type LAM-based oscillators, including the memristor emulator, are presented. Both simulation and experimental results demonstrate the practicability of the proposed mathematical model and the validity of the theoretical analysis.
In this paper, outer synchronization between drive and response networks via adaptive impulsive pinning control is investigated. In the pinning control scheme, the controlled nodes are changed adaptively according to the synchronization errors at different impulsive instants. Based on the Lyapunov function method and mathematical analysis, a synchronization criterion is precisely derived. Under this criterion, the impulsive intervals for achieving outer synchronization of two given networks are estimated. Further, an adaptive strategy is designed for a node-to-node pinning impulsive controller, with a corresponding synchronization condition derived. In the proposed adaptive control scheme, the impulsive instants adjust themselves to the needed values as time goes on, and an algorithm for determining the impulsive instants is developed and evaluated. The theoretical results are illustrated to be effective by several numerical examples.
This paper reports an autonomous-system-based approach for creating compound chaotic attractors from a class of generalized Lorenz systems via switching control. A state variable scale transformation is proposed for these systems to ensure that all attractors have comparable sizes. Coordinate transformation in the z-axis direction is also used, so that every pair of adjacent chaotic attractors have a common connected domain in the same phase space. Then, by switching control, the intended compound chaotic attractors can be generated. A circuit for a compound Lorenz–Chen–Lü chaotic attractor is designed and implemented for demonstration, which verifies the effectiveness of the proposed simulation-based technique. The aim of this report is to demonstrate the possibility of accomplishing such a very challenging task, leaving the extremely difficult underlying theory to future studies.
Naming game simulates the process of naming an object by a single word, in which a population of communicating agents can reach global consensus asymptotically through iteratively pair-wise conversations. We propose an extension of the single-word model to a multi-word naming game (MWNG), simulating the case of describing a complex object by a sentence (multiple words). Words are defined in categories, and then organized as sentences by combining them from different categories. We refer to a formatted combination of several words as a pattern. In such an MWNG, through a pair-wise conversation, it requires the hearer to achieve consensus with the speaker with respect to both every single word in the sentence as well as the sentence pattern, so as to guarantee the correct meaning of the saying; otherwise, they fail reaching consensus in the interaction. We validate the model in three typical topologies as the underlying communication network, and employ both conventional and man-designed patterns in performing the MWNG.
This technical note studies distributed adaptive control of synchronization in complex networks. An effective distributed adaptive strategy to tune the coupling weights of a network is designed based on local information of node dynamics. The analysis is then extended to the case where only a small fraction of coupling weights can be adjusted. A general criterion is derived and it is found that synchronization can be reached if the subgraph consisting of the edges and nodes corresponding to the updated coupling weights is connected. Finally, simulation examples are given to illustrate the theoretical analysis.
In this paper, we prove that chaos in the sense of Li–Yorke and of Devaney is prevalent in discrete systems admitting the so-called heteroclinical repellers, which are similar to the transversely heteroclinical orbits in both continuous and discrete systems and are corresponding to the snap-back repeller proposed by Marotto for proving the existence of chaos in higher-dimensional systems. In addition, the concept of heteroclinical repellers is generalized to be applicable to the case with degenerate transformations. In the end, some illustrative examples are provided to illustrate the theoretical results.
No abstract is provided for this article.
This article offers an overview of rational approximation theory and its applications in systems engineering. The importance of rational approximation theory in systems engineering and signal processing can be easily understood from the observation that all the transfer functions (matrices) of linear time-invariant systems and digital filters are rational functions (matrices). Rational approximation has a long history in the field of approximation theory, an important and active branch of mathematics, and has found very broad applications in control and systems engineering.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
