Stochastic synchronization of coupled neural networks with intermittent control

In this Letter, we study the exponential stochastic synchronization problem for coupled neural networks with stochastic noise perturbations. Based on Lyapunov stability theory, inequality techniques, the properties of Weiner process, and adding different intermittent controllers, several sufficient conditions are obtained to ensure exponential stochastic synchronization of coupled neural networks with or without coupling delays under stochastic perturbations. These stochastic synchronization criteria are expressed in terms of several lower-dimensional linear matrix inequalities (LMIs) and can be easily verified. Moreover, the results of this Letter are applicable to both directed and undirected weighted networks. A numerical example and its simulations are offered to show the effectiveness of our new results.     

Synchronization Scheme for Uncertain Chaotic Systems via RBF Neural Network

A sliding mode adaptive synchronization controller is presented with a neural network of radial basis function （RBF） for two chaotic systems. The uncertainty of the synchronization error system is approximated by the RBF neural network. The synchronization controller is given based on the output of the RBF neural network. The proposed controller can make the synchronization error convergent to zero in 5s and can overcome disruption of the uncertainty of the system and the exterior disturbance. Finally, an example is given to illustrate the effectiveness of the proposed synchronization control method.     

Increasing-order Projective Synchronization of Chaotic Systems with Time Delay

This work is concerned with lag projective synchronization of chaotic systems with increasing order. The systems under consideration have unknown parameters and different structures. Combining the adaptive control method and feedback control technique, we design a suitable controller and parameter update law to achieve lag synchronization of chaotic systems with increasing order. The result is rigorously proved by the Lyapunov stability theorem. Moreover, corresponding simulation results are given to verify the effectiveness of the proposed methods.     

A Novel Adaptive Observer-Based Control Scheme for Synchronization and Suppression of a Class of Uncertain Chaotic Systems

A novel adaptive observer-based control scheme is presented for synchronization and suppression of a class of uncertain chaotic system. First, an adaptive observer based on an orthogonal neural network is designed. Subsequently, the sliding mode controllers via the proposed adaptive observer are proposed for synchronization and suppression of the uncertain chaotic systems. Theoretical analysis and numerical simulation show the effectiveness of the proposed scheme.     

Adaptive Synchronization between Two Different Complex Networks with Time-Varying Delay Coupling

A new general network model for two complex networks with time-varying delay coupling is presented. Then we investigate its synchronization phenomena. The two complex networks of the model differ in dynamic nodes, the number of nodes and the coupling connections. By using adaptive controllers, a synchronization criterion is derived. Numerical examples are given to demonstrate the effectiveness of the obtained synchronization criterion. This study may widen the application range of synchronization, such as in chaotic secure communication.     

Projective Synchronization in Time-Delayed Chaotic Systems

For the first time, we report on projective synchronization between two time delay chaotic systems with single time delays. It overcomes some limitations of the previous work, where projective synchronization has been investigated only in finite-dimensional chaotic systems, so we can achieve projective synchronization in infinitedimensional chaotic systems. We give a general method with which we can achieve projective synchronization in time-delayed chaotic systems. The method is illustrated using the famous delay-differential equations related to optical bistability. Numerical simulations fully support the analytical approach.     

Enhancing synchronizability by weight randomization on regular networks

In weighted networks, redistribution of link weights can effectively change the properties of networks, even though the corresponding binary topology remains unchanged. In this paper, the effects of weight randomization on synchronization of coupled chaotic maps is investigated on regular weighted networks. The results reveal that synchronizability is enhanced by redistributing of link weights, i.e. coupled maps reach complete synchronization with lower cost. Furthermore, we show numerically that the heterogeneity of link weights could improve the complete synchronization on regular weighted networks.     

Synchronization Control of Two Different Chaotic Systems with Known and Unknown Parameters

Chaos synchronization of two different chaotic systems with known and unknown parameters is studied. Based on the Lyapunov stability theory, two different chaotic systems with known parameters realize global synchronization via the successfully designed nonlinear controller. By employing an adaptive synchronization scheme, the synchronization of two different chaotic systems with unknown parameters is achieved. Numerical simulations validate the effectiveness of the theoretical analysis.     

Investigation of a Unified Chaotic System and Its Synchronization by Simulations*

We investigate a unified chaotic system and its synchronization including feedback synchronization and adaptive synchronization by numerical simulations. We propose a new dynamical quantity denoted by K, which connects adaptive synchronization and feedback synchronization, to analyze synchronization schemes. We find that K can estimate the smallest coupling strength for a unified chaotic system whether it is complete feedback or one-sided feedback. Based on the previous work, we also give a new dynamical method to compute the leading Lyapunov exponent.     

Synchronization and control of chaos in coupled chaotic multimode Nd:YAG lasers

In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.     

Projective cluster synchronization in drive-response dynamical networks

In this paper, we study the projective cluster synchronization in a drive-response dynamical network with 1+N coupled partially linear chaotic systems. Because the scaling factors characterizing the dynamics of projective synchronization remain unpredictable, pinning control ideas are adopted to direct the different scaling factors onto the desired values. It is also shown that the projection cluster synchronization can be realized by controlling only one node in each cluster. Numerical simulations on the chaotic Lorenz system are illustrated to verify the theoretical results.     

Experimental Investigation of Chaos Synchronization in DFB Diode Lasers with Unsymmetrical Scheme

We experimentally generate high dimension chaotic waveforms with smooth spectrum using a distributed feedback （DFB） semiconductor laser with unidirectional fibre ring long-cavity feedback, and implement the stable chaos synchronization when the chaotic light is injected into a solitary DFB laser diode. The synchronization quality is investigated by time-domain and frequency-domain analysis separately, The frequency-domain analysis indicates that the synchronization has higher quality in the high frequency band. The influences of the injection strength and the frequency detuning on the synchronization are measured. Our experimental results show that the robust synchronization can be maintained with the optical frequency detuning from -11GHz to 40 GHz.     

Synchronization of Kuramoto oscillators in random complex networks

We study the synchronization of coupled phase oscillators in random complex networks. The topology of the networks is assumed to be vary over time. Here we mainly study the onset of global phase synchronization when the topology switches rapidly over time. We find that the results are, to some extent, different from those in deterministic situations. In particular, the synchronizability of coupled oscillators can be enhanced in ER networks and scale-free networks under fast switching, while in stochastic small-world networks such enhancement is not significant.     

A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances

In this Letter, the synchronization problem is investigated for a class of stochastic complex networks with time delays. By utilizing a new Lyapunov functional form based on the idea of ‘delay fractioning’, we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the globally asymptotically mean-square synchronization of the addressed delayed networks with stochastic disturbances. These sufficient conditions, which are formulated in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The main results are proved to be much less conservative and the conservatism could be reduced further as the number of delay fractioning gets bigger. A simulation example is exploited to demonstrate the advantage and applicability of the proposed result.     

Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity

In this Letter, the concept of practical synchronization is introduced and the chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity is investigated. Based on the time-domain approach, a tracking control is proposed to realize chaos synchronization for the uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity. Moreover, the guaranteed exponential convergence rate and convergence radius can be pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.     

Stochastic linear generalized synchronization of chaotic systems via robust control

In this Letter, based on robust control, we provide a general theoretical result on stochastic linear generalized synchronization (GS) of chaotic systems. Given a driving system with noise perturbations and a linear synchronization function, a response system is developed easily according to the scheme derived here. By introducing the Lyapunov stability theory and linear matrix inequalities (LMIs), the condition for synchronization is proved to be effective. Finally, the Lorenz system is taken for illustration and verification.     

Detecting synchronization in coupled stochastic ecosystem networks

Instantaneous phase difference, synchronization index and mutual information are considered in order to detect phase transitions, collective behaviours and synchronization phenomena that emerge for different levels of diffusive and reactive activity in stochastic networks. The network under investigation is a spatial 2D lattice which serves as a substrate for Lotka-Volterra dynamics with 3rd order nonlinearities. Kinetic Monte Carlo simulations demonstrate that the system spontaneously organizes into a number of asynchronous local oscillators, when only nearest neighbour interactions are considered. In contrast, the oscillators can be correlated, phase synchronized and completely synchronized when introducing different interactivity rules (diffusive or reactive) for nearby and distant species. The quantitative measures of synchronization show that long distance diffusion coupling induces phase synchronization after a well defined transition point, while long distance reaction coupling induces smeared phase synchronization.     

Function projective synchronization of different chaotic systems with uncertain parameters

This Letter investigates the function projective synchronization of different chaotic systems with unknown parameters. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function. Numerical simulations on Lorenz system and Newton-Leipnik system are presented to verify the effectiveness of the proposed scheme.     

Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects

The paper studies the exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects based on the unidirectional linear coupling scheme. Some sufficient conditions are established by the stability analysis of impulsive differential equations. An illustrative example is provided to show the effectiveness and feasibility of the proposed method and results.     

Impulsive control of projective synchronization in chaotic systems

Scaling factor of projective synchronization in coupled partially linear chaotic systems is hardly predictable. To control projective synchronization of chaotic systems in a preferred way, an impulsive control scheme is introduced to direct the scaling factor onto a desired value. The control approach is derived from the impulsive differential equation theory. Numerical simulations on the chaotic Lorenz system are illustrated to verify the theoretical results. Furthermore, some interesting and surprising numerical results are discussed.