Generalized synchronization of spatiotemporal chaos in a weighted complex network

The nodes of the network are composed of the spatiotemporal chaos systems. The relations between the nodes are built through a weighted connection and the nonlinear terms of the chaos systems themselves are taken as coupling functions. The structure of the coupling functions between the connected nodes and the range of the control gain are obtained based on Lyapunov stability theory. It is proven that generalized chaos synchronization of the weight complex network can be realized even if the coupling strength between the nodes is adopted as any weight value. Subsequently, the catalytic reaction diffusion system which has spatiotemporal chaos behavior is taken as example, and simulation results show the effectiveness of the synchronization principle.     

Study on spatiotemporal chaos synchronization among complex networks with diverse structures

The spatiotemporal chaos synchronization among complex networks with diverse structures is investigated. The spatiotemporal chaos systems are taken as the nodes of networks and constructed as some networks with diverse structures. The conditions of global synchronization among networks and the coupling function to be determined among diverse networks are discussed and confirmed based on stability theory. The Burgers equation with many practice physics processes, such as turbulent flow and heat-transfer, is adopted for example to imitate the experiment. It is found that the synchronization performance among all networks is very stable.     

Parameter identification and synchronization of spatiotemporal chaos in uncertain complex network

Synchronization and parameter identification of a unidirectional star-network constructed by discrete spatiotemporal chaos systems with unknown parameters are studied. The synchronization principle of the network and design method of parameter recognition law are introduced. The function to be determined in the parameter recognition law and the range of adjusting parameter are obtained based on Lyapunov stability theory. Not only global synchronization of the network is realized, but also the unknown parameters in spatiotemporal chaos systems at the nodes of the network are identified. Discrete laser spatiotemporal chaos model is taken as each node of the network, and simulation results show the effectiveness of the synchronization principle and parameter recognition law.     

Projective synchronization of a class of complex network based on high-order sliding mode control

Projective synchronization of a class of complex networks is investigated using second-order sliding mode control. The sliding surface and the control input are designed based on stability theory. The Burgers system with spatiotemporal chaotic behavior in the physics domain is taken as nodes to constitute the complex network, and the Fisher–Kolmogorov system is taken as the tracking target. The artificial simulation results show that the synchronization technique is effective.     

Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system

In this paper, we introduce a new chaotic complex nonlinear system and study its dynamical properties including invariance, dissipativity, equilibria and their stability, Lyapunov exponents, chaotic behavior, chaotic attractors, as well as necessary conditions for this system to generate chaos. Our system displays 2 and 4-scroll chaotic attractors for certain values of its parameters. Chaos synchronization of these attractors is studied via active control and explicit expressions are derived for the control functions which are used to achieve chaos synchronization. These expressions are tested numerically and excellent agreement is found. A Lyapunov function is derived to prove that the error system is asymptotically stable.     

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures is investigated. The identification law of unknown parameters and the adaptive law of the configuration matrix element in state equations of network nodes are determined based on stability theory, and the conditions of realizing spatiotemporal chaos synchronization between uncertain complex networks with different structures are discussed and obtained. Further, the Fisher–Kolmogorov system with spatiotemporal chaotic behavior is taken as the nodes of drive and response networks to imitate the experiment. It is found that the synchronization performance between two networks is very stable.     

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.     

Zero-lag chaos synchronization properties in a hierarchical tree-type network consisting of mutually coupled semiconductor lasers

Nonlinear Dynamics - Chaos synchronization properties in a novel hierarchical tree-type optical network consisting of semiconductor lasers (SLs) are investigated numerically. In such network, each...     

Fractional-order complex T system: bifurcations,chaos control,and synchronization

In this paper, the fractional-order complex T system is proposed. The dynamics of the system including symmetry, the stability of equilibrium points, bifurcations with variation of system parameters, and derivative orders are investigated. Period-doubling and tangent bifurcations with appropriate derivative orders and system parameters are observed. Besides, the control problem of the system is examined by using the feedback control technique. Furthermore, based on the stability theory of fractional-order systems, the scheme of function projective synchronization for the fractional-order complex T system is presented. The function projective synchronization for the system is realized by designing an appropriate synchronization controller. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.     

Pinning adaptive synchronization of complex dynamical network with multi-links

Networks with multi-links are universal in the real world such as communication networks, transport networks, and social networks. It is important for us to investigate the control of complex dynamical network with multi-links. In this paper, both local and global stabilities of dynamical network with multi-links are analyzed by applying adaptive control theory and mathematical tools, and some new criteria are proposed to ensure the pinning synchronization. We find that the number of pinned nodes satisfies an inequality for synchronization. Additionally, we solve the problem of how much the coupling strength we need to achieve network synchronization with one pinned node in the network system with multi-links. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.     

Adaptive coupling synchronization in complex network with uncertain boundary

It is difficult that all the boundaries of chaotic system were estimated precisely; this is why the coupling coefficient cannot be determined beforehand in the problem of synchronization of complex networks. Thus, an estimation of coupling coefficient should be given before designing some controllers. In addition, to realize the synchronization, the estimated coupling coefficient has to be large enough. However, it is not true that the larger the coupling coefficient the better the synchronization is. In fact, a coupling coefficient which is larger than what it needs to be means the energy waste. To overcome this difficulty, in this paper we propose an adaptive coupling method. And a new concept about asymptotic stability is presented. Numerical simulations are implemented on different complex networks. The results indicate that the synchronization can be achieved without a large estimated coefficient.     

An image blocks encryption algorithm based on spatiotemporal chaos

In this paper, the CML-based spatiotemporal chaos system is used for image blocks encryption, which gets higher security. The basic idea is to divide the image into blocks, and then use the block numbers as the spatial parameter of CML to iterate the chaos system. Each lattice generates a chaos sequence, and the number of chaos sequence values is equal to the pixels number of each block. The chaos sequences and the former block plaintext codecide the substitution and diffusion of each block. Simulation results show that the performance and security of the proposed encryption system can encrypt the image effectively and resist various typical attacks.     

Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes

A fractional-order weighted complex network consists of a number of nodes, which are the fractional-order chaotic systems, and weighted connections between the nodes. In this paper, we investigate generalized chaotic synchronization of the general fractional-order weighted complex dynamical networks with nonidentical nodes. The well-studied integer-order complex networks are the special cases of the fractional-order ones. Based on the stability theory of linear fraction-order systems, the nonlinear controllers are designed to make the fractional-order complex dynamical networks with distinct nodes asymptotically synchronize onto any smooth goal dynamics. Numerical simulations are provided to verify the theoretical results. It is worth noting that the synchronization effect sensitively depends on both the fractional order ?? and the feedback gain k _i . Moreover, generalized synchronization of the fractional-order weighted networks can still be achieved effectively with the existence of noise perturbation.     

Projective synchronization of nonlinear-coupled spatiotemporal chaotic systems

The projective synchronization of one-dimensional discrete spatiotemporal chaotic systems is discussed in this paper. The coupling equation is determined by suitably separating the linear term and the nonlinear term of the dynamic function, and two coupled map lattices reach projective synchronization by the nonlinear-coupling method. Besides, this method is expanded to the projective synchronization of the complex network composed by coupled map lattices. Numerical simulations show the effectiveness of the scheme.     

The synchronization of general complex dynamical network via pinning control

In this paper, the globally synchronization of the general complex network is investigated. Firstly, we discuss the synchronization problem of the linearly coupled and directed network under the pinning control, and make comparison with the previous work about the undirected network. Sufficient conditions are obtained to guarantee the realization of synchronization. Secondly, the synchronization problem of nonlinearly coupled and undirected network under the pinning control is studied, and a criteria of getting synchronization is given. Furthermore, we introduced the adaptive adjustment of the coupling strength in nonlinearly coupled network. At last, we give simulation examples to verify our theoretical results.     

Pinning synchronization of complex network with non-derivative and derivative coupling

This paper investigates synchronization of a complex network with non-derivative and derivative coupling. For achieving the pinning synchronization, the corresponding controllers are designed and applied to only a small fraction of nodes. Both linear and adaptive feedback control methods are used to design controllers. Based on Lyapunov stability theory, several simple and useful criteria for pinning synchronization are derived. Finally, numerical simulations are given to verify the effectiveness of the derived results.     

Adaptive synchronization of an uncertain coupling complex network with time-delay

This paper proposes a new complex dynamical network model, in which the nodes are coupled with time-delay, and the inner coupling matrices are with uncertain forms. This model can describe the real world more realistically and can be widely used in practical engineering application. Synchronization in the proposed network model is analyzed by the Lyapunov stability theory and some adaptive controllers are designed to ensure that the proposed network achieve local and global synchronization, respectively. Theoretical analysis and numerical simulations fully verify the main results.     

On CML model for study of spatiotemporal chaos

A new coupled map lattic(CML)model is given by using some stability analysis for the related difference equations.Numerical results show that the new model is.an effective one of studying spatiotemporal chaos,especially for strongly coupled systems.