This paper is concerned with master-slave synchronization of chaotic Φ6 Duffing oscillators by using linear state error feedback control. Compared with some existing methods and results, this paper estimates the bound of the first trajectory (variable) of the controlled slave system and uses this bound to derive synchronization criteria for two chaotic Φ6 Duffing oscillators. The effectiveness of synchronization criteria is illustrated by three simulation examples.

This paper is concerned with synchronization of congestion control models for underwater wireless sensor networks. Compared with some existing papers, the main contribution of this paper is that synchronization schemes for congestion control models are constructed and used to control the chaos in underwater wireless sensor networks. The conditions for positive solutions of congestion control models are derived. Some bounds of solutions of congestion control models are estimated. Moreover, two synchronization criteria are derived by using two different congestion controls. Furthermore, the conservative analysis of two synchronization criteria is achieved. Two examples are used to illustrate the effectiveness of synchronization control results.

Complexity is the undeniable part of the natural systems providing them with unique and wonderful capabilities. Memristor is known to be a fundamental block to generate complex behaviors. It also is reported to be able to emulate synaptic long-term plasticity as well as short-term plasticity. Synaptic plasticity is one of the important foundations of learning and memory as the high-order functional properties of the brain. In this study, it is shown that memristive neuronal network can represent plasticity phenomena observed in biological cortical synapses. A network of neuronal units as a two-dimensional excitable tissue is designed with 3-neuron Hopfield neuronal model for the local dynamics of each unit. The results show that the lattice supports spatiotemporal pattern formation without supervision. It is found that memristor-type coupling is more noticeable against resistor-type coupling, while determining the excitable tissue switch over different complex behaviors. The stability of the resulting spatiotemporal patterns against noise is studied as well. Finally, the bifurcation analysis is carried out for variation of memristor effect. Our study reveals that the spatiotemporal electrical activity of the tissue concurs with the bifurcation analysis. It is shown that the memristor coupling intensities, by which the system undergoes periodic behavior, prevent the tissue from holding wave propagation. Besides, the chaotic behavior in bifurcation diagram corresponds to turbulent spatiotemporal behavior of the tissue. Moreover, we found that the excitable media are very sensitive to noise impact when the neurons are set close to their bifurcation point, so that the respective spatiotemporal pattern is not stable.

This paper is concerned with designing feedback controllers for master-slave synchronization of two chaotic memristor-based Chua's circuits. The memductance function of memristor-based Chua's circuits is a bounded function with a bounded derivative which is more generalized than those piecewise constant-valued functions or quadratic functions in some existing papers. The main contributions are that one master-slave synchronization criterion is established for two chaotic memristor-based Chua's circuits, and the feedback controller gain is easily obtained by solving a set of linear matrix inequalities. One numerical example is given to illustrate the effectiveness of the design method.

This paper is concerned with master-slave synchronization of 4D hyperchaotic Rabinovich systems. Compared with some existing papers, this paper has two contributions. The first contribution is that the nonlinear terms of error systems remained which inherit nonlinear features from master and slave 4D hyperchaotic Rabinovich systems, rather than discarding nonlinear features of original hyperchaotic Rabinovich systems and eliminating those nonlinear terms to derive linear error systems as the control methods in some existing papers. The second contribution is that the synchronization criteria of this paper are global rather than local synchronization results in some existing papers. In addition, those synchronization criteria and control methods for 4D hyperchaotic Rabinovich systems are extended to investigate the synchronization of 3D chaotic Rabinovich systems. The effectiveness of synchronization criteria is illustrated by three simulation examples.

This paper investigates synchronization of coupled neural-mass models. Compared with some existing papers which study the dynamical behaviors of single neural-mass model, some synchronization criteria of coupled neural-mass models are derived. Moreover, the adjacency coupling for neural-mass models is investigated, which is more generalized than the special coupling in some existing papers. Furthermore, those derived synchronization criteria can be used to study synchronization of neural-mass models with special coupling Two simulation examples are used to reveal the effectiveness of derived synchronization criteria.

This paper deals with the mixed synchronization (coexistence of synchronization and antisynchronization) of two chaotic financial systems. Two mixed synchronization criteria for two chaotic financial systems are derived with a single controller and without external controls, respectively. In addition, the control method and synchronization criteria are applied to study the mixed synchronization of a class of modified chaotic financial systems. Three examples are used to illustrate the effectiveness of our derived results.

This article is concerned with master–slave synchronization for two chaotic Hindmarsh–Rose neurons. The main contribution of this article is that three synchronization criteria are derived by using linear feedback control without the estimation of bounds of state variables of controlled slave neurons. Three simulation examples are used to illustrate the effectiveness of our results. © 2015 Wiley Periodicals, Inc. Complexity 21: 319–327, 2016

This paper studies chaotic synchronization of modified discrete-time Tinkerbell systems. By constructing the Lyapunov function and using the linear feedback control, some synchronization criteria for modified discrete-time Tinkerbell systems are derived. The conservativeness of those synchronization criteria is compared. The effectiveness of derived results is demonstrated by six examples.

This paper is concerned with synchronization of two coupled Hind-marsh-Rose (HR) neurons.Two synchronization criteria are derived by using nonlinear feedback control and linear feedback control, respectively.A synchronization criterion for FitzHugh-Nagumo (FHN) neurons is derived as the application of control method of this paper.Compared with some existing synchronization results for chaotic systems, the contribution of this paper is that feedback gains are only dependent on system parameters, rather than dependent on the norm bounds of state variables of uncontrolled and controlled HR neurons.The effectiveness of our results are demonstrated by two simulation examples.

In this paper, a new unidirectional coupling for global synchronization of two Hindmarsh-Rose neurons is designed. Compared with existing results, external control for global synchronization is no longer required. A synchronization criterion of two Hindmarsh-Rose neurons with rigorous mathematical proof is derived. An example is given to illustrate the effectiveness of the obtained result.

Some mathematical models in engineering and physics, such as rotating pendulums, governors and phase locked loops in circuits, can be described as nonautonomous systems in which there exist chaotic attractors. This paper investigates master-slave synchronization for two nonautonomous chaotic systems by using time-delayed feedback control. Firstly, three delay-dependent synchronization criteria, which are formulated in the form of linear matrix inequalities (LMIs), are established for complete synchronization, lag synchronization and anticipating synchronization, respectively. Secondly, sufficient conditions on the existence of a time-delayed feedback controller are derived by employing these newly-obtained synchronization criteria. The controller gain can be obtained by solving a set of LMIs. Finally, the synchronization criteria and the design method are applied to master-slave synchronization for rotating pendulum systems.

This paper is concerned with master–slave synchronization for two identical non-autonomous horizontal platform systems by using time-delay feedback control. Compared with some existing results on synchronization for horizontal platform systems, the effect of the time delay in the feedback control on master–slave synchronization is investigated. Applying a delay decomposition approach, some delay-dependent synchronization criteria are established and formulated in the form of linear matrix inequalities (LMIs). Sufficient conditions about the existence of a time delay feedback controller are derived by employing these newly obtained synchronization criteria. The controller gains can be achieved by solving a set of LMIs. One simulation example is given to illustrate the effectiveness of synchronization criteria and the design method.

This paper is concerned with the global synchronization in Lur'e complex dynamical networks. Compared with the existing complex dynamical networks with the time delay either in every node or in coupling part, this class of Lur'e complex dynamical networks not only have the time-delayed nodes, but also have the time-delayed coupling. These two classes of time delays are different from each other. By using LMI technique, synchronization criteria of this class of Lur'e complex dynamical networks are derived. These synchronization criteria are delay-dependent not only for the time delay in every node, but also for the time delay in the coupling part. A numerical example demonstrates the effectiveness of synchronization results.

This paper is to design time-varying delay feedback controllers for outer synchronization between two complex dynamical networks with nonidentical coupling structures. By constructing the Lur'e-Postnikov Lyapunov functional, a new delay-dependent synchronization criterion is derived and formulated in the form of linear matrix inequalities (LMIs). Then, sufficient conditions on the existence of a time-varying delay feedback controller are obtained by using this newly-obtained synchronization criterion. The controller gains can be derived. A numerical example is given to illustrate the effectiveness of the synchronization criteria and the design method.

This paper focuses on master-slave synchronization for two identical chaotic labyrinth systems with different initial conditions by using time-delay feedback control. By employing the differential mean value theorem to deal with the nonlinear term of the error system, the error system is modeled as a polytopic system. Applying a delay decomposition approach, a delay-dependent synchronization criterion is established and formulated in the form of linear matrix inequalities (LMIs). A sufficient condition about the existence of a time delay feedback controller is derived by employing this newly-obtained synchronization criterion. The controller gain can be achieved by solving a set of LMIs. One simulation example is used to illustrate the effectiveness of the synchronization criterion and the design method.

This paper investigates the effects of coupling delays on synchronization in Lur'e complex dynamical networks. Every identical node in the network can be represented as a Lur'e system. Based on Lyapunov–Krasovskii functionals and Lur'e–Postnikov Lyapunov functionals, some delay-dependant synchronization criteria are derived by employing a delay decomposition approach. A Lur'e complex dynamical network with Chua's circuit nodes and one numerical example are given to illustrate the effectiveness of the synchronization criteria.