Almost sure synchronization for nonlinear complex stochastic networks with Lévy noise

Nonlinear Dynamics - In this paper, almost sure synchronization is developed for a class of nonlinear complex stochastic networks with an adaptive feedback control. This class of networks are...     

Cluster synchronization analysis of complex dynamical networks by input-to-state stability

Cluster synchronization is an interesting issue in complex dynamical networks with community structure. In this paper, we study cluster synchronization of complex networks with non-identical systems by input-to-state stability. Some sufficient conditions that ensure cluster synchronization of complex networks are provided. We show that the cluster synchronization is difficult to achieve if there are some links among different clusters. The analysis is then extended to the case where the outer coupling strengths are adaptive. Finally, numerical simulations are given to validate our theoretical analysis.     

Adaptive exponential synchronization in pth moment for stochastic time varying multi-delayed complex networks

In this paper, the analysis problem of adaptive exponential synchronization in pth moment is considered for stochastic complex networks with time varying multi-delayed coupling. By using the Lyapunov–Krasovskii functional, stochastic analysis theory, several sufficient conditions to ensure the mode adaptive exponential synchronization in pth moment for stochastic delayed complex networks are derived. To illustrate the effectiveness of the synchronization conditions derived in this paper, a numerical example is finally provided.     

Exponential synchronization of stochastic delayed discrete-time complex networks

This paper is concerned with the problem of synchronization for stochastic discrete-time drive-response networks with time-varying delay. By employing the Lyapunov functional method combined with the stochastic analysis as well as the feedback control technique, several sufficient conditions are established that guarantee the exponentially mean-square synchronization of two identical delayed networks with stochastic disturbances. These sufficient conditions, which are expressed in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. A particular feature of the LMI-based synchronization criteria is that they are dependent not only on the connection matrices in the drive networks and the feedback gains in the response networks, but also on the lower and upper bounds of the time-varying delay, and are therefore less conservative than the delay-independent ones. Two numerical examples are exploited to demonstrate the feasibility and applicability of the proposed synchronization approaches.     

Global synchronization of stochastic delayed complex networks

This paper is concerned with the delay-dependent synchronization criterion for stochastic complex networks with time delays. Firstly, expectations of stochastic cross terms containing the It? integral are investigated by utilizing stochastic analysis techniques. In fact, in order to obtain less conservative delay-dependent conditions for stochastic delay systems including stochastic complex (or neural) networks with time delays, how to deal with expectations of these stochastic cross terms is an important problem, and expectations of these stochastic terms were not dealt with properly in many existing results. Then, based on the investigation of expectations of stochastic cross terms, this paper proposes a novel delay-dependent synchronization criterion for stochastic delayed complex networks. In the derivation process, the mathematical development avoids bounding stochastic cross terms. Thus, the method leads to a simple criterion and shows less conservatism. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

A new approach to almost-sure asymptotic stability of stochastic systems of higher dimension

The almost sure asymptotic stability of higher-dimensional linear stochastic systems and of a special class of nonlinear stochastic systems with homogeneous drift and diffusion coefficients of order one is studied. Based on the well-known Khasminskii's theorem, a new approach for obtaining the regions of almost sure asymptotic stability and instability without evaluating the stationary probability density of the diffusion process defined on unit hypersphere is proposed. Two examples of two and three degree-of-freedom linear stochastic systems are given to illustrate the application and effectiveness of the proposed approach combined with stochastic averaging.     

Almost sure state estimation for nonlinear stochastic systems with Markovian switching

In this paper, the almost sure asymptotic stability is investigated for the state estimation problem of a general class of nonlinear stochastic systems with Markovian switching. A nonlinear state estimator with Markovian switching is first proposed, and then, a sufficient condition is given, which guarantees the almost sure asymptotic stability of the dynamics of the estimation error. Based on this condition, some simplified criteria are deduced by taking special forms of Lyapunov functions. Subsequently, an easy-to-verify procedure is put forward for the state estimation problem of the linear stochastic system with Markovian switching. Finally, two numerical examples are used to illustrate the effectiveness of the main results.     

Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix

In this paper, we investigate the cluster synchronization problem for networks with nonlinearly coupled nonidentical dynamical systems and asymmetrical coupling matrix by using pinning control. We derive sufficient conditions for cluster synchronization for any initial values through a feedback scheme and propose an adaptive feedback algorithm that adjusts the coupling strength. Some numerical examples are then given to illustrate the theoretical results.     

Almost sure stability condition of weakly coupled linear nonautonomous random systems

In this study, the sufficient condition of almost sure stability of twodimensional oscillating systems under parametric excitations is investigated. The systems considered are assumed to be composed of two weakly coupled subsystems. The driving actions are considered to be stationary stochastic processes satisfying ergodic properties. The properties of quadratic forms are used in conjunction with the bounds for the eigenvalues to obtain, in a closed form, the sufficient condition for the almost sure stability of the systems.     

Stochastic synchronization of complex network via a novel adaptive nonlinear controller

In this paper, a novel adaptive nonlinear controller is designed to achieve stochastic synchronization of complex networks. We find that this novel adaptive nonlinear controller is less conservative and may be more widely used than the traditional adaptive linear controller. By using the properties of Weiner process, the stochastic synchronization of complex networks with stochastic perturbation via the proposed novel adaptive nonlinear controller can be achieved. Experimental tests demonstrate the superior performance of this novel adaptive nonlinear controller as compared to a conventional adaptive linear controller.     

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

In this paper, we are concerned with the synchronization problem of a class of stochastic reaction-diffusion neural networks with time-varying delays and Dirichlet boundary conditions. By using the Lyapunov–Krasovskii functional method, feedback control approach and stochastic analysis technology, delay-dependent synchronization conditions including the information of reaction-diffusion terms are presented, which are expressed in terms of linear matrix inequalities (LMIs). The feedback controllers can be constructed by solving the derived LMIs. Finally, illustrative examples are given to show the effectiveness of the proposed technique.     

Adaptive synchronization of stochastic neural networks with mixed time delays and reaction–diffusion terms

In this paper, the problem of exponential synchronization is investigated for a class of stochastic perturbed chaotic neural networks with both mixed time delays and reaction?Cdiffusion terms. By employing Lyapunov?CKrasovskii functional and stochastic analysis approaches, an adaptive controller is designed to guarantee the exponential synchronization of proposed neural networks in the mean square. In particular, the mixed time delays in this paper synchronously consist of constant delay in the leakage term (i.e., ??leakage delay??), discrete time-varying delay and distributed time-varying delay which are more general than those discussed in the previous literature. Furthermore, our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. Therefore, the results obtained in this paper generalize and improve those given in the previous literature. Finally, the extensive simulations are performed to show the effectiveness and feasibility of the obtained method.     

Almost sure stochastic stability of a viscoelastic double-beam system

This paper investigates the dynamic stability of a viscoelastic double-beam system under parametric excitations. It is assumed that the two beams, made from Voigt–Kelvin material, are simply supported and continuously joined by a Winkler elastic layer. Each pair of axial forces consists of a constant part and a time-dependent stochastic function. In the case of “non-white” excitations, by using the direct Liapunov method, bounds of the almost sure stability of the double-beam system as a function of retardation time, bending stiffness, stiffness modulus of the Winkler layer, variances of the stochastic forces and the intensity of the deterministic components of axial loading are obtained. Numerical calculations are performed for the Gaussian process with a zero mean, as well as a harmonic process with a random phase. When the excitations are wideband noises, almost sure stability is obtained within the concept of the Liapunov exponent. White noise and Ornstein–Uhlenbeck processes are considered as models of wideband noises.     

Finite-time stochastic synchronization of time-delay neural networks with noise disturbance

Nonlinear Dynamics - The finite-time stochastic synchronization of time-delay neural networks with noise disturbance is investigated according to finite-time stability theory of stochastic...     

<Emphasis Type="Italic">p</Emphasis>th moment exponential synchronization for stochastic delayed Cohen–Grossberg neural networks with Markovian switching

This paper is a contribution to the analysis of the pth moment exponential synchronization problem for a class of stochastic delayed Cohen–Grossberg neural networks with Markovian switching. The jumping parameters are determined by a continuous-time, discrete-state Markov chain, and the delays are time-varying delays.     

Noise-induced outer synchronization between two different complex dynamical networks

In this paper, based on the theory of stochastic differential equations, we study the outer synchronization between two different complex dynamical networks with noise coupling. The theoretical result shows that two different complex networks can achieve generalized outer synchronization only with white-noise-based coupling. Numerical examples further verify the effectiveness and feasibility of the theoretical results. Numerical evidence shows that the synchronization rate is proportional to the noise intensity.     

Exponential synchronization of Markovian jumping complex dynamical networks with randomly occurring parameter uncertainties

This paper investigates the mean-square exponential synchronization problem of complex dynamical networks with Markovian jumping and randomly occurring parameter uncertainties. The considered Markovian transition rates are assumed to be partially unknown. The parameter uncertainties are considered to be random occurrence and norm-bounded, and the randomly occurring parameter uncertainties obey certain Bernoulli-distributed white noise sequences. Based on the Lyapunov method and stochastic analysis, by designing mode-dependent feedback controller, some sufficient conditions are presented to ensure the mean-square exponential synchronization of Markovian jumping complex dynamical networks with partly unknown transition rates and randomly occurring parameter uncertainties. Numerical examples are given to demonstrate the validity of the theoretical results.     

二阶线性随机微分方程的渐近稳定性

对刚度系数是遍历过程的二阶线性随机微分方程，本文研究了其平凡解几乎处处渐近稳定性问题。利用刚度系数导数过程的性质，给出了平凡解几乎处处渐近稳定的充分条件。当刚度系数是遍历高斯过程或周期过程时，还具体计算了其渐进稳定区域。结果表明，本文结果改进了目前有关的渐近稳定性的条件。     

Cluster synchronization of linearly coupled complex networks via linear and adaptive feedback pinning controls

Cluster synchronization is investigated for complex networks via linear and adaptive feedback control strategies. It is shown that two different controllers can be designed to achieve the cluster synchronization. Unlike most existing papers, we need not nondelayed and delayed coupling matrices to be symmetric or irreducible. Finally, two examples are given to illustrate the effectiveness of the proposed methods.     

Cluster synchronization of overlapping uncertain complex networks with time-varying impulse disturbances

Nonlinear Dynamics - This paper addresses the scheme of cluster synchronization of overlapping uncertain complex networks with time-varying impulse disturbances. Many existing works on cluster...