This paper studies synchronization via pinning control on general complex dynamical networks, such as strongly connected networks, networks with a directed spanning tree, weakly connected networks, and directed forests. A criterion for ensuring network synchronization on strongly connected networks is given. It is found that the vertices with very small in-degrees should be pinned first. In addition, it is shown that the original condition with controllers can be reformulated such that it does not depend on the form of the chosen controllers, which implies that the vertices with very large out-degrees may be pinned. Then, a criterion for achieving synchronization on networks with a directed spanning tree, which can be composed of many strongly connected components, is derived. It is found that the strongly connected components with very few connections from other components should be controlled and the components with many connections from other components can achieve synchronization even without controls. Moreover, a simple but effective pinning algorithm for reaching synchronization on a general complex dynamical network is proposed. Finally, some simulation examples are given to verify the proposed pinning scheme.
In this paper, the dynamical behaviors of a class of weighted local-world evolving networks with aging nodes are investigated. As the network grows, each newly added node is connected to some existing nodes through strength–age preferential attachment. Each time step, the newly added node with randomly determined initial degree is connected to some existing nodes through a local strength–age preferential attachment. By using tools from stochastic analysis and continuous approximation, it is theoretically proved that the strength distribution of the generated network has a power-law form with exponent depending nontrivially on a decay factor α ∈ [ 0 , 1 ) . In addition, the clustering coefficient, correlation and small-world properties of this class of networks are examined via simulations. It is shown that clustering coefficient is a monotone decreasing function of the decay factor, and the assortative degree correlation and small-world properties appear simultaneously. Finally, the new model is used to characterize the Internet topology as a typical application.
Very recently, a new method of generating hyperchaos via a simple periodic forcing signal was introduced and a new hyperchaotic system was formulated by controlling a three-dimensional autonomous Chen chaotic system with a periodic driving signal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">γcos(ωt)</i> . The hyperchaotic attractor is not only verified with bifurcation analysis but also demonstrated by computer simulations. In this paper, we further investigate its bifurcation behaviors and electronic circuit implementation. A good qualitative agreement between the simulation and the experimental results is observed.
An effective method of chaotification via time-delay feedback for a simple finite-dimensional continuous-time autonomous system is made rigorous in this paper. Some mathematical conditions are derived under which a nonchaotic system can be controlled to become chaotic, where the chaos so generated is in a rigorous mathematical sense of Li–Yorke in terms of the Marotto theorem. Numerical simulations are given to verify the theoretical analysis.
The chaotic behaviors in the fractional order unified system are numerically investigated. By utilizing the fractional calculus techniques, we found that chaos exists in the fractional order unified system with order less than 3. The lowest order we found to have chaos in this system is 2.76. Chaos synchronization of the fractional order unified system is theoretically and numerically studied using the one-way coupling method. The suitable conditions for achieving synchronization of the fractional order differential system are derived by using the Laplace transform theory. It is noticed that the time required for achieving synchronization of the drive system and the response system and the synchronization effect sensitively depend on the coupling strength. Numerical simulations are performed to verify the theoretical analysis.
In this brief, robust adaptive control of unknown modified Cohen-Grossberg neural networks with time delays is considered based on nonsmooth analysis and matrix inequality technique. Several new controllers are designed to ensure the global asymptotical stability of the targeted equilibrium point. The designed controllers are independent of the bounds of the perturbations, system functions and the time delays. One does not need to know the bounds of the unknown parameters, but only needs to know the structures of the modified Cohen-Grossberg neural networks with time delays. Finally, some simulations examples are given to verify the theoretical results.
In process industry, there exist many Wiener systems with input magnitude constraints for which, however, most of the existing control algorithms cannot guarantee to have sufficiently large regions of asymptotic stability. In this paper, the subspace method is applied to separate the nonlinear and linear blocks in a constrained multi‐input/multi‐output (MIMO) Wiener system and a novel dual‐mode nonlinear model predictive control algorithm is developed to maximize the region of the asymptotic stability. Simulation results are presented to demonstrate the virtues of this new control algorithm. The limitation is the requirement that the state and input matrices of the Wiener system's linear block should be accurately identified. Copyright © 2009 John Wiley & Sons, Ltd.
Optimization aims at finding optimal solution(s) from all feasible solutions, where an optimal solution represents the extremum with respect to a certain objective. This chapter introduces an evolving approach for generating benchmark testing problems. It also introduces a systematic method for constructing performance-comparison-based benchmark problems, namely the hierarchical-fitness-based evolving benchmark generator (HFEBG). The chapter describes the HFEBG framework, together with two variants, namely HFEBG-U and HFEBG-H. It utilises U-test and H-test in different hierarchical-fitness assignment methods. Testing optimization algorithms on both real-world problems and benchmark problems would give a performance measure. Performance comparison of optimization algorithms is studied in terms of unique difficulty: specifically, uniquely easy and uniquely difficult problems. A criticism has been expressed in the field, namely, many proposed novel optimization algorithms actually contribute little, since they are not compared with the winners of competitions. Sequential learnable evolutionary algorithm provides an algorithm-selection framework for solving black-box continuous design-optimization problems.
In this paper, the Parameter Switching (PS) algorithm is used to approximate numerically attractors of a Hopfield Neural Network (HNN) system. The PS algorithm is a convergent scheme designed for approximating attractors of an autonomous nonlinear system, depending linearly on a real parameter. Aided by the PS algorithm, it is shown that every attractor of the HNN system can be expressed as a convex combination of other attractors. The HNN system can easily be written in the form of a linear parameter dependence system, to which the PS algorithm can be applied. This work suggests the possibility to use the PS algorithm as a control-like or anticontrol-like method for chaos.
Frequency-modulated differential chaos shift keying (FM-DCSK) is a non-coherent modulation and demodulation technique, which uses a chaotic signal as the carrier. Due to the inherent broadband nature, its good performance of anti-multipath interference is quite promising in wireless communications. In order to improve the overall performance of this chaos-based system, LDPC (low density parity check) codes are proposed to use for enhancing the FM-DCSK communication system. Through system design and simulations, it is shown that the enhanced system is superior to that without LDPC codes by at least 8 dB over an AWGN channel. Moreover, the longer the frame, the greater its coding gain.
In this paper, we present a new approach for chaos reproduction using variable structure recurrent neural networks (VSRNN). A neural network identifier is designed, with a variable structure that will change according to its output performance as compared to the given orbits of an unknown chaotic systems. A tradeoff between identification errors and computational complexity is discussed.
This paper introduces a novel four-order system, which can generate one-directional (1-D) n-torus, two-directional (2-D) n /spl times/ m-torus, three-directional (3-D) n /spl times/ m /spl times/ l-torus, four-directional (4-D) n /spl times/ m /spl times/ l /spl times/ p-torus chaotic attractors. Furthermore, a novel block circuit diagram is designed for the hardware implementation of multi-directional grid multi-torus chaotic attractors. This is the first time in the literature to experimentally verify a 5 /spl times/ 5 /spl times/ 3 /spl times/ 3-torus chaotic attractors.
This paper is mainly concerned with a class of nonautonomous discrete systems (<i>X</i>,<i>f</i><sub>1,∞</sub>). New definitions of proximity relations and sensitivity in nonautonomous discrete systems are given. Some relations among <i>P</i>(<i>f</i><sub>1,∞</sub>), <i>L</i>(<i>f</i><sub>1,∞</sub>), <i>R</i>(<i>f</i><sub>1,∞</sub>), <i>S</i>(<i>f</i><sub>1,∞</sub>) and <i>P</i>(<i>f</i><sub>1,∞</sub>)(<i>x</i>) are derived. And some chaotic properties of <i>f</i><sub>1,∞</sub> are proved.
We describe a computational method, known as the Nevanlinna algorithm, for the matrix-valued Nevanlinna-Pick interpolation. The original interpolation problem formulated using the Carathéodory class of matrix-valued rational functions is first converted to an equivalent setting using the Schur class of rational functions. As a result, the necessary and sufficient Pick's condition for the interpolation becomes consistent with the scalar-valued formulation, so that some efficient techniques developed for the scalar-valued interpolation can be employed or modified for the matrix-valued case. We give a brief, yet sufficiently clear, derivation and a detailed arithmetic complexity analysis for the algorithm. We show that an n-point matrix-valued Nevanlinna-Pick interpolation using the new algorithm requires approximately 95nm 3 complex arithmetic operations, where m is the matrix dimension.
In this paper, we propose a modified susceptible–infected–susceptible model with an infective medium, which describes epidemics transmitted through an infective medium on complex networks. We examine epidemic thresholds for disease spreading by using this new model and compare it with the standard SIS model and another SIS model having an infective medium. We also study and compare the effects of the uniform immunization scheme on different models. We finally give some necessary and sufficient conditions for the global stability of the new model.
