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The study of the synchronous stability of two coupled Rössler attractors sometimes can be effectively described by approximating the trajectory on the attractor as a planar outward spiral. We show that this is true only when one is dealing with the spiral-type attractor. But when the equally important funnel-type attractor is encountered, a properly constructed time-weighted average must be used to yield a prediction that agrees well with numerical results. We also show analytically how the separation vector evolves in time, and demonstrate why this study matters when one tries to perform the time-weighted average. [ABSTRACT FROM AUTHOR]

In this paper, the identification problem of fractional-order chaotic systems is proposed and investigated via an evolutionary optimization approach. Different with other studies to date, this research focuses on the identification of fractional-order chaotic systems with not only unknown orders and parameters, but also unknown initial values and structure. A group of fractional-order chaotic systems, i.e., Lorenz, Lü, Chen, Rössler, Arneodo and Volta chaotic systems, are set as the system candidate pool. The identification problem of fractional-order chaotic systems in this research belongs to mixed integer nonlinear optimization in essence. A powerful evolutionary algorithm called composite differential evolution (CoDE) is introduced for the identification problem presented in this paper. Extensive experiments are carried out to show that the fractional-order chaotic systems with unknown initial values and structure can be successfully identified by means of CoDE. [ABSTRACT FROM AUTHOR]

A new coupling scheme for anticipating synchronization of chaotic systems is proposed. The scheme consists of a master system and two in series coupled slave systems with periodically switching parameters. The scheme does not require the presence of any time-delay terms either in a master or in slave systems and provides long-term anticipation. The value of anticipation time as well as the conditions of synchronization are derived in an analytical form. Analytical results are tested by numerical experiments with the chaotic Rössler and Lorenz systems as well as the Hindmarsh–Rose neuron in a regime of chaotic bursting. Also a robustness of the scheme with respect to parameter mismatch and noise is demonstrated. [ABSTRACT FROM AUTHOR]

Abstract: We introduce a chaos model for a permanent-magnet synchronous motor and construct a coupled chaotic motor in a complex dynamic network using the Newman–Watts small-world network algorithm. We apply adaptive pinning control theory for complex networks to obtain suitable adaptive feedback gain and the number of nodes to be pinned. Nodes of low degree are pinned to realize global asymptotic synchronization in the complex network. The proposed adaptive pinning controller is added to the complex motor network for simulation and verification. [Copyright &y& Elsevier]

Abstract: This Letter is concerned with the problem of fuzzy modeling and synchronization of memristor-based Lorenz circuits with memristor-based Chuaʼs circuits. In this Letter, a memristor-based Lorenz circuit is set up, and illustrated by phase portraits and Lyapunov exponents. Furthermore, a new fuzzy model of memristor-based Lorenz circuit is presented to simulate and synchronize with the memristor-based Chuaʼs circuit. Through this new fuzzy model, two main advantages can be obtained as: (1) only two linear subsystems are needed; (2) fuzzy synchronization of these two different chaotic circuits with different numbers of nonlinear terms can be achieved with only two sets of gain K. Finally, numerical simulations are used to illustrate the effectiveness of these obtained results. [Copyright &y& Elsevier]

Abstract: We report experimental evidence of mixed synchronization in two unidirectionally coupled chaotic oscillators using a scalar coupling. In this synchronization regime, some of the state variables may be in complete synchronization while others may be in anti-synchronization state. We extended the theory by using an adaptive controller with an updating law based on Lyapunov function stability to include parameter fluctuation. Using the scheme, we implemented a cryptographic encoding for digital signal through parameter modulation. [Copyright &y& Elsevier]

Abstract: We study dynamics of two bistable Hénon maps coupled in a master-slave configuration. In the case of coexistence of two periodic orbits, the slave map evolves into the master map state after transients, which duration determines synchronization time and obeys a power law with respect to the coupling strength. This scaling law is almost independent of the map parameter. In the case of coexistence of chaotic and periodic attractors, very complex dynamics is observed, including the emergence of new attractors as the coupling strength is increased. The attractor of the master map always exists in the slave map independently of the coupling strength. For a high coupling strength, complete synchronization can be achieved only for the attractor similar to that of the master map. [Copyright &y& Elsevier]

Abstract: In this Letter, analytical conditions for the sinusoidal synchronization of the pendulum and Duffing oscillator are presented. From the analytical conditions, the invariant domain of such sinusoidal synchronization is determined, and the control parameter map of the synchronicity is achieved. Under specific parameters, numerical illustrations of the partial and full sinusoidal synchronizations of the controlled Duffing oscillator with the pendulum are carried out for a better understanding of such synchronization under specific function constraints. The methodology presented in this Letter is applicable to synchronizations with any specific function constraints. [Copyright &y& Elsevier]

Abstract: This Letter investigates chaos synchronization of chaotic and hyperchaotic systems. Based on finite-time stability theory, a simple adaptive control method for realizing chaos synchronization in a finite time is proposed. In comparison with previous methods, the present method is not only simple, but could also be easily utilized in application. Numerical simulations are given to illustrate the effectiveness and validity of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this Letter, a new lag projective synchronization for fractional-order chaotic (hyperchaotic) systems is proposed, which includes complete synchronization, anti-synchronization, lag synchronization, generalized projective synchronization. It is shown that the slave system synchronizes the past state of the driver up to a scaling factor. A suitable controller for achieving the lag projective synchronization is designed based on the stability theory of linear fractional-order systems and the pole placement technique. Two examples are given to illustrate effectiveness of the scheme, in which the lag projective synchronizations between fractional-order chaotic Rössler system and fractional-order chaotic Lü system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results. [Copyright &y& Elsevier]

Abstract: In this Letter, two adaptive controllers are proposed for the lag-synchronization of two non-identical time-delayed chaotic systems with fully unknown parameters. Based on Lyapunov-stability theorem and adaptive techniques, sufficient conditions for the lag-synchronization of these two systems are discussed. Finally, illustrative examples are given to verify the validity of the developed controllers. [Copyright &y& Elsevier]

Abstract: In this Letter we compare the characteristics of two types of the intermittent behavior (type-I intermittency in the presence of noise and eyelet intermittency taking place in the vicinity of the chaotic phase synchronization boundary) supposed hitherto to be different phenomena. We show that these effects are the same type of dynamics observed under different conditions. The correctness of our conclusion is confirmed by the consideration of different sample systems, such as quadratic map, Van der Pol oscillator and Rössler system. Consideration of the problem concerning the upper boundary of the intermittent behavior also confirms the validity of the statement on the equivalence of type-I intermittency in the presence of noise and eyelet intermittency observed in the onset of phase synchronization. [Copyright &y& Elsevier]

Abstract: This Letter addresses a nonlinear robust adaptive control that utilizes linear matrix inequalities for asymptotic synchronization of two coupled chaotic FitzHugh–Nagumo neurons under unknown parameters and uncertain stimulation current amplitudes and phase shifts. Synchronization of chaotic neurons using the proposed control method through numerical simulation is demonstrated. [Copyright &y& Elsevier]

Abstract: In this Letter, the complex dynamical networks with community structure and nonidentical nodes are considered. The globally asymptotical synchronization of the time-delayed complex community networks onto any uniformly smooth state is studied. Some simple and useful criteria are derived by constructing an effective control scheme and adjusting automatically the adaptive coupling strength. Finally, the developed techniques are applied to two complex community networks which are respectively synchronized to a chaotic trajectory and a periodic orbit, and numerical simulations are provided to show the feasibility of the developed methods. [ABSTRACT FROM AUTHOR]

Abstract: This Letter investigates synchronization of two nonidentical Lur''e systems with time-varying delay and parameter mismatches via impulsive control. Based on the theory of impulsive functional differential equations, sufficient conditions for impulsive synchronization with a bound on the synchronization error are derived. An illustrative example is provided to validate the proposed method. [Copyright &y& Elsevier]

Abstract: We dissect Rössler equation and give a linear core, which can capture the essence of Rössler oscillator. The maximal transversal Lyapunov exponents calculated from the core are in good agreement with those obtained from Rössler equation. The idea is also tested for coupled Chua''s circuit systems. Numerical experiments are given. [Copyright &y& Elsevier]

Abstract: This Letter reports phase diagrams quantifying and contrasting the dynamical performance of the paradigmatic piecewise-linear and cubic circuits of Chua. Although both circuits may be regarded as macroscopically isomorphic over wide regions in control parameter space, we show that their microscopic structure displays a myriad of rather distinctive intrinsic features making them unique. Inhomogeneities embedded in periodic and chaotic phases complicate some applications of the circuits but may also adequately act as realistic noise proxies in synchronization problems. In addition, infinite cascades of spirals and hubs observed experimentally very recently in a related dissipative flow are shown to be also present in both circuits of Chua, emerging however in a rather distinctive asymmetric way. Thus Chua''s circuits may be used to study experimentally elusive and theoretically intricate phenomena generating periodicity hubs. [Copyright &y& Elsevier]

Abstract: In this Letter, a high gain integral controller for synchronization of unknown non-autonomous chaotic systems is proposed. Perturbation theory is used to demonstrate that the synchronization error of the resulting feedback system converges to zero. Numerical simulations are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This Letter investigates the problem of adaptive lag synchronization and parameters adaptive lag identification of chaotic systems. In comparison with those of existing parameters identification schemes, the unknown parameters are identified by adaptive lag laws, and the delay time is also identified in this Letter. Numerical simulations are also given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this Letter, dual synchronization in modulated time delay system using delay feedback controller is proposed. Based on Lyapunov stability theory, we suggest a general method to achieve the dual-anticipating, dual, dual-lag synchronization of time-delayed chaotic systems and we find both its existing and sufficient stability conditions. Numerically it is shown that the dual synchronization is also possible when driving system contain two completely different systems. Effect of parameter mismatch on dual synchronization is also discussed. As an example, numerical simulations for the Mackey–Glass and Ikeda systems are conducted, which is in good agreement with the theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract: The dynamics of weakly coupled chaotic maps in which the connections are rewired randomly with varying probability P and rewiring period T is investigated. In contrast to rapidly switched random links enhancing spatiotemporal regularity in strong-coupling regime, rewiring the network with certain rewiring period T contributes to the stability of synchronized cycles in a weak-coupling range, the reason of which is that unstable kink-patterns emerge and need some time steps to vanish. Furthermore, the synchronized basin size B for different period T is given. We observed an interesting phenomenon that basin B is relatively large when T is even in the range of small values of T. Finally, the synchronizing efficiency with respect to T is discussed and we found is the most efficient. [Copyright &y& Elsevier]

Abstract: A new method for secure information transmission based on generalized synchronization is proposed. The principal advantage of it is a remarkable stability to noise. To reveal this peculiarity of the proposed method the effectiveness of the detection of the information signal from the transmitted one in the presence of noise in the communication channel is examined both for the proposed scheme and for the schemes of chaotic communication known already. The main ideas of the proposed method are illustrated by the example of coupled Rössler systems used both transmitter and receiver. [Copyright &y& Elsevier]

Abstract: The proposed anti-synchronization conditions of coupled chaotic systems are based, in this Letter, on the use of aggregation techniques for the stability study of the error dynamics. The schemes are, successfully, applied to coupled Rössler and Chen chaotic systems making the instantaneous characteristic matrix under the arrow form. Numerical simulations are performed to illustrate the efficiency of the proposed approach. [Copyright &y& Elsevier]

Abstract: This Letter investigates the stabilization and synchronization of Genesio–Tesi systems. Firstly, modifying the previous method, we stabilize the Genesio–Tesi system. Then, we synchronize two identical Genesio chaotic system by extending the obtained stabilization results. To the best of our knowledge, the above controllers obtained in this Letter are simpler than those obtained in the existing results. Finally, numerical simulations verify the effectiveness and the validity of the above theoretical results. [Copyright &y& Elsevier]

Abstract: The synchronization transition is studied in delay-coupled logistic maps. For low coupling, in-phase and out-of-phase synchronous dynamics coexist, and with increasing coupling there is a regime of quasiperiodicity before eventual attraction to a fixed point at a critical value of coupling that depends on the nonlinearity. The presence of a region of asynchrony separating two synchronized regimes—termed anomalous behaviour—has been observed earlier in continuous systems and is shown here to occur in delay mappings as well. There are regions of in-phase, anti-phase, and out-of-phase dynamics of periodic as well as chaotic attractors. [Copyright &y& Elsevier]

Abstract: The Letter develops an adaptive impulsive scheme that includes a sole restriction criterion to achieve synchronization of chaotic nonlinear systems with unknown parameters. The system is assumed to satisfy the local Lipschitz condition while a Lipschitz constant and the uncertain system parameters are estimated by augmented adaptation equations. Adaptation of all parameters is proven to converge exponentially. The significance of the related control parameters and their margins in the criterion is also discussed in detail. The Lorenz system has been simulated to illustrate the theoretical analysis. [Copyright &y& Elsevier]

Abstract: Recently introduced modified function projective synchronization (MFPS) in which chaotic systems synchronize up to a scaling function matrix has important applications in secure communications. We design coupling function for unidirectional coupling in identical and mismatched hyperchaotic oscillators to realize MFPS through Open-Plus-Closed-Loop (OPCL) coupling method. The arbitrary scaling function matrix elements are properly chosen such that we can produce function projective synchronization, synchronization, anti-synchronization and amplitude death on desired states of the response system simultaneously. Numerical simulations on identical hyperchaotic Rossler and mismatched hyperchaotic Lu system are presented to verify the effectiveness of the proposed scheme. A secure communication scheme based on MFPS is also presented. [Copyright &y& Elsevier]

Abstract: This Letter deals with the exponential synchronization problem of coupled chaotic systems with time delay by means of periodically intermittent feedback control. Different from the differential inequality approach adopted in the previous literature, we resort to the Lyapunov–Razumikhin methodology in order to derive a new exponential synchronization criterion for delayed chaotic systems. Furthermore, all the constraints imposed in these references are removed and no transcendental equation is involved. Therefore, the application scope is enlarged and the result is computationally efficient for the obtained condition. Two kinds of chaotic systems, Ikeda and Lu systems, are provided to demonstrate our theoretical results and the superiority over the existing ones. [Copyright &y& Elsevier]

Abstract: Isochronal synchronisation between the elements of an array of three mutually coupled directly modulated semiconductor lasers is utilized for the purpose of simultaneous bidirectional secure communication. Chaotic synchronisation is achieved by adding the coupling signal to the self feedback signal provided to each element of the array. A symmetric coupling is effective in inducing synchronisation between the elements of the array. This coupling scheme provides a direct link between every pair of elements thus making the method suitable for simultaneous bidirectional communication between them. Both analog and digital messages are successfully encrypted and decrypted simultaneously by each element of the array. [Copyright &y& Elsevier]

Abstract: The modified function projective lag synchronization (MFPLS) is proposed in this Letter, in which the states of two chaotic systems are asymptotically lag synchronized up to a desired scaling function matrix. Based on Lyapunov stability theory, a general method of MFPLS is investigated. The scheme is successfully applied to two groups examples, which are the MFPLS between Lorenz system and Lü system, and two identical hyper-chaotic Chen system. Corresponding numerical simulations are performed to verify and illustrate the analytical results. [Copyright &y& Elsevier]

Abstract: In this Letter, an output error feedback control scheme is addressed for synchronization of a class of non-autonomous chaotic systems based on the drive-response framework. A fuzzy disturbance observer is used to compensate for the difference between the structures of two different systems. To compensate for the uncertainty caused by the unknown phase difference between the drive and the response systems, an adaptive control scheme is employed that is based on the Lyapunov stability theory. Numerical simulations are presented to illustrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: Synchronization of fractional-order nonlinear systems has received considerable attention for many research activities in recent years. In this Letter, we consider the synchronization between two nonidentical fractional-order systems. Based on the open-plus-closed-loop control method, a general coupling applied to the response system is proposed for synchronizing two nonidentical incommensurate fractional-order systems. We also derive a local stability criterion for such synchronization behavior by utilizing the stability theory of linear incommensurate fractional-order differential equations. Feasibility of the proposed coupling scheme is illustrated through numerical simulations of a limit cycle system, a chaotic system and a hyperchaotic system. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: The Letter studies the projective synchronization of a class of delayed chaotic systems. The drive-response system can be synchronized to within a desired scaling factor via impulsive control. Some sufficient conditions are derived by the stability analysis of the impulsive functional differential equations. An illustrative example is provided to show the effectiveness and feasibility of the proposed method and results. [Copyright &y& Elsevier]

Abstract: This Letter focuses on the master–slave synchronization problem of the unified chaotic systems. Based on Lyapunov stability theory and linear matrix inequality (LMI) formulation, a simple linear feedback control law is obtained to make the state of two identical unified chaotic systems asymptotically synchronized. Simulation results have illustrated the effectiveness of the proposed chaos synchronization solution. [Copyright &y& Elsevier]

Abstract: In this Letter, an adaptive control scheme is developed to study the anti-synchronization behavior between two identical and different chaotic systems with unknown parameters. This adaptive anti-synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. The adaptive anti-synchronization between two identical systems (Chen system) and different systems (Genesio and Lü systems) are taken as two illustrative examples to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are shown to verify the results. [Copyright &y& Elsevier]

Abstract: In this letter, a new fractional-order hyperchaotic system is proposed. By utilizing the fractional calculus theory and computer simulations, it is found that hyperchaos exists in the new fractional-order four-dimensional system with order less than 4. The lowest order to have hyperchaos in this system is 2.88. The results are validated by the existence of two positive Lyapunov exponents. Using the pole placement technique, a nonlinear state observer is designed to synchronize a class of nonlinear fractional-order systems. The observer method is used to synchronize two identical fractional-order hyperchaotic systems. In addition, the active control technique is applied to synchronize the new fractional-order hyperchaotic system and the fractional-order Chen hyperchaotic system. The two schemes, based on the stability theory of the fractional-order system, are rather simple, theoretically rigorous and convenient to realize synchronization. They do not require the computation of the conditional Lyapunov exponents. Numerical results are performed to verify the effectiveness of the proposed synchronization schemes. [Copyright &y& Elsevier]

Abstract: This Letter studies the existence of Hölder continuity of generalized synchronization (GS). The model considered here includes three bidirectionally coupled chaotic systems, two of them denote the driving systems, while the other stands for the response system. Based on the modified system approach, GS is classified into several types, and two kinds therein are investigated. By using the Schauder fixed point theorem, sufficient conditions for the existence of Hölder continuous GS are derived and theoretically proved. In addition, numerical examples are given for verification. [Copyright &y& Elsevier]

Abstract: In virtue of techniques derived from nonlinear control system theory, we establish conditions under which one could obtain anticipating synchronization between two periodically driven deterministic ratchets that are able to exhibit directed transport with a finite velocity. Criteria are established in order to guarantee the anticipating synchronization property of such systems as well as characterize phase space dynamics of the ratchet transporting behaviors. These results allow one to predict the chaotic direct transport features of particles on a ratchet potential using a copy of the same system that performs as a slave, which are verified through numerical simulation. [Copyright &y& Elsevier]

Abstract: This Letter presents fuzzy model-based robust tracking control for the adaptive synchronization of uncertain chaotic systems. Fuzzy model and adaptive algorithm are employed to present the unknown chaotic systems. and sliding mode control are combined to construct a robust tracking controller. The incorporated controller can attenuate the external disturbance and approximation error to any prescribed level. The proposed scheme guarantees that all the variables are bounded and the tracking error is compensated. [Copyright &y& Elsevier]

Abstract: This work investigates function projective synchronization of two-cell Quantum-CNN chaotic oscillators using adaptive method. Quantum-CNN oscillators produce nano scale chaotic oscillations under certain conditions. By Lyapunove stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers. [Copyright &y& Elsevier]

Abstract: A high precision fast projective synchronization method was proposed through introducing an impact factor. The numerical simulations indicate that the synchronization precision was increased three orders of magnitude higher than available methods in literature, under the same conditions of numerical method and hardware. The synchronization can achieved after first iteration. The synchronization speed has been increased by 13 484 times and 23 000 times when and , respectively, compared to general methods. [Copyright &y& Elsevier]

Abstract: In this Letter, we propose a new anti-synchronization scheme for a general class of chaotic systems. Based on Lyapunov theory and linear matrix inequality (LMI) approach, for the first time, the anti-synchronization controller is presented to not only guarantee stable anti-synchronization but also reduce the effect of external disturbance to an norm constraint. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed anti-synchronization scheme. [Copyright &y& Elsevier]

Abstract: By introducing a control strength matrix, the active control theory in chaotic synchronization is developed. With this extended method, chaos complete synchronization can be achieved more easily, i.e., a much smaller control signal is enough to reach synchronization in most cases. Numerical simulations on Rossler, Liu''s four-scroll, and Chen system confirmed this and show that the synchronization result depends on the control strength significantly. Especially, in the case of Liu and Chen systems, the response systems'' largest Lyapunov exponents'' variation with the control strength is not monotone and there exist minima. It is novel for Chen system that the synchronization speed with a special small strength is higher than that of the usual active control which, as a special case of the extended method, has a much larger control strength. All these results indicate that the control strength is an important factor in the actual synchronization. So, with this extended active control, one can make a better and more practical synchronization scheme by adjusting the control strength matrix. [Copyright &y& Elsevier]

Abstract: The notion of chaotic phase synchronization (CPS) in the large-scale delayed scale-free network is discussed in this Letter. The amplitude death (AD) phenomenon is observed and analyzed in terms of energy. AD occurs when the time-delay becomes long enough. The adaptive coupling scheme has better performance in CPS and AD compared with the constant scheme, and simulation results confirm conclusions. [Copyright &y& Elsevier]

Abstract: Five interesting experiments have been done for a class of chaos synchronization systems with unknown parameters and unknown control directions. And three important conclusions about parameters identification have been made. First, a necessary and sufficient condition for parameters identification is obtained. Second, a Nussbaum method is proposed to solve the problem of unknown control direction. Third, the adaptive method is not infinitely effective considered for our current ability of computation and simulation algorithm. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Anomalous phase synchronization in nonidentical interacting oscillators is manifest as the increase of frequency disorder prior to synchronization. We show that this effect can be enhanced when a time-delay is included in the coupling. In systems of limit-cycle and chaotic oscillators we find that the regions of phase disorder and phase synchronization can be interwoven in the parameter space such that as a function of coupling or time-delay the system shows transitions from phase ordering to disorder and back. [Copyright &y& Elsevier]

Abstract: This Letter considers synchronization of a general class of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance to an norm constraint. A dynamic feedback control scheme is proposed for synchronization in chaotic systems for the first time. Then, a criterion for existence of the controller is given in terms of LMIs. Finally, a numerical simulation is presented to show the effectiveness of the proposed chaos synchronization scheme. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]