Projective Synchronization Research Articles

Memristor-based novel complex-valued chaotic system and its projective synchronisation using nonlinear active control technique

In this paper, a flux controlled memristor-based novel complex-valued chaotic system and its projective synchronisation is investigated. The proposed complex-valued chaotic system has line and plane of equilibria, i.e. an infinite number of equilibria. Different qualitative and quantitative tools such as time series, phase plane, Poincare section, Lyapunov exponents, Lyapunov spectrum, and Lyapunov dimension are used to evidence the chaotic behaviour of the proposed complex-valued system. Further, the projective synchronisation between the proposed complex-valued chaotic systems is achieved using nonlinear active control. Active control laws are designed, by using sum of the relevant variables of the proposed complex-valued chaotic systems, to ensure the convergence of error dynamics. The required global asymptotic stability condition is derived using Lyapunov stability theory. Simulation is done in MATLAB environment to verify the theoretical approach. Simulation results reveal that the objectives of the paper are achieved successfully.

A new memristive model with complex variables and its generalized complex synchronizations with time lag

The point of this paper is to display and explore a memristive complex hyperchaotic model with a flux-controlled memristor. The model’s behavior is examined through numerical simulations by utilizing some tools of nonlinear theory, for example, generalized Hamiltonian, symmetry, dissipative, equilibria and their stability, bifurcation diagram, and Lyapunov exponents. Next, this paper centers around the complex function projective lag synchronization (CFPLS) for various-dimensional hyperchaotic models with complex variables and uncertain parameters. A simulation model displays the effectiveness of the obtained values. The effects of CFPLS were used to develop a precise application in secure correspondence. The digital outcomes were used to verify the adequacy and feasibility of the exhibited technique.

Mixed H_{infty }/passive exponential function projective synchronization of delayed neural networks with hybrid coupling based on pinning sampled-data control

This paper presents the problem of mixed H_{infty }/passive exponential function projective synchronization of delayed neural networks with constant discrete and distributed delay couplings under pinning sampled-data control scheme. The aim of this work is to focus on designing of pinning sampled-data controller with an explicit expression by which the stable synchronization error system is achieved and a mixed H_{infty }/passive performance level is also reached. Particularly, the control method is designed to determine a set of pinned nodes with fixed coupling matrices and strength values, and to select randomly pinning nodes. To handle the Lyapunov functional, we apply some new techniques and then derive some sufficient conditions for the desired controller existence. Furthermore, numerical examples are given to illustrate the effectiveness of the proposed theoretical results.

Multi-switching combination synchronization of spatiotemporal coupled chaotic systems with complexities

In this paper, multi-switching combination synchronization for spatiotemporal coupled systems are studied. For the local system in spatiotemporal coupled systems, different local dynamic behaviors are taken into consideration. With the Backstepping method, synchronization controllers are designed for different possible combined errors and corresponding theorems are derived according to the Lyapunov stability theory. In the stability design, multi-switching combination synchronizations can be translated into corresponding combination projective synchronization with different projective factors. In addition, complexities including time delays are considered in the synchronization process. At last, simulation results show the robustness and effectiveness of our methods.

On New Generalized Hybrid Synchronization in Chaotic and Hyperchaotic Discrete-time Dynamical Systems

In this paper, by combining full state hybrid projective synchronisation (FSHPS) and inverse full state hybrid projective synchronisation (IFSHPS), we generalize the idea of hybrid chaos synchronization in discrete-time. Based on stability theory of linear discrete-time systems and Lyapunov stability theory, new approaches are proposed to investigate the new type of hybrid synchronization between chaotic maps of different dimensions. Several numerical examples have highlighted the effectiveness of the novel approaches developed herein.

Adaptive hybrid function projective synchronization of chaotic systems with fully unknown periodical time-varying parameters

In this paper, an adaptive learning control approach is presented for the hybrid functional projective synchronization (HFPS) of different chaotic systems with fully unknown periodical time-varying parameters. Differential-difference hybrid parametric learning laws and an adaptive learning control law are constructed via the Lyapunov–Krasovskii functional stability theory, which make the states of two different chaotic systems asymptotically synchronized in the sense of mean square norm. Moreover, the boundedness of the parameter estimates are also obtained. The Lorenz system and Chen system are illustrated to show the effectiveness of the hybrid functional projective synchronization scheme.

Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays

This sequel is concerned with the analysis of projective lag synchronization of Riemann–Liouville sense fractional order memristive BAM neural networks (FOMBNNs) with mixed time delays via hybrid controller. Firstly, a new type of hybrid control scheme, which is the combination of open loop control and adaptive state feedback control is designed to guarantee the global projective lag synchronization of the addressed FOMBNNs model. Secondly, by using a Lyapunov–Krasovskii functional and Barbalet’s lemma, a new brand of sufficient criterion is proposed to ensure the projective lag synchronization of the FOMBNNs model considered. Moreover, as special cases by using a hybrid control scheme, some sufficient conditions are derived to ensure the global projective synchronization, global complete synchronization and global anti-synchronization for the FOMBNNs model considered. Finally, numerical simulations are provided to check the accuracy and validity of our obtained synchronization results.

Hybrid Projective Synchronization of Fractional-order Neural Networks with Different Dimensions

This paper is concerned with the problem of hybrid projective synchronization between two fractional-order neural networks with the order lying in the interval \((1,2)\). The coupled networks have ...

Fixed-time projective synchronization of memristive neural networks with discrete delay

In this paper, the fixed-time projective synchronization of memristive neural networks (MNNs) with discrete delay is studied for the first time. In the circuit implementation of memristive neural network, the synapses are modeled by memristors. Compared with common neural networks, memristive neural network can simulate the human brain better. The fixed-time controller designed in this paper is simplest among all the controllers that are used to study fixed-time stability/synchronization. Since fixed-time stability, fixed-time synchronization and fixed-time anti-synchronization are all special cases of fixed-time projective synchronization, some existing results about the stability/synchronization of MNNs can be regarded as the corollaries of our theoretical results. Numerical simulations are provided to verify the theoretical results.

Finite-time projective synchronization of fractional-order complex-valued memristor-based neural networks with delay

This paper studies the finite-time projective synchronization of fractional-order complex-valued memristor-based neural networks (FCVMNNs) with delay. By applying the set-valued map, the differential inclusion theory and Gronwall–Bellman integral inequalities, some sufficient criteria are established to achieve the finite time projective synchronization of the FCVMNNs. The upper bound of the settling time for synchronization is also estimated. Moreover, two numerical examples are designed to verify the correctness and effectiveness of the obtained theoretical results.

Complex Projection Synchronization of Fractional-Order Complex-Valued Memristive Neural Networks with Multiple Delays

In this paper, the complex projection synchronization problem of fractional-order complex-valued memristive neural networks is investigated, in which the projection factor is set to complex value and multiple time delays are considered. Under the framework of set-valued mapping and differential inclusion theory, a hybrid control strategy is designed to analyze the complex projection synchronization problem of the system. Moreover, some criterion to ensure the synchronization of drive response network is obtained by applying the stability theorem and comparison principle of the fractional order systems with multiple time delays. Finally, numerical simulation example is provided to verify the correctness and effectiveness of the complex projection synchronization strategy.

Combined projective synchronization for a class of time-delayed hyperchaotic systems via active control

We investigate combined projective synchronization for a class of time-delayed chaotic systems related to optical bistable or hybrid optical bistable devices. We overcome some limitations of previous works, where only combined complete synchronization can be achieved. Based on the Lyapunov asymptotical stability theory and active control technology, the effective sufficient conditions derived to ensure the combined projective synchronization for a class of time-delayed hyperchaotic systems can be investigated. The efficiency and effectiveness of the proposed method have been verified with several numerical simulations using well-known time-delayed chaotic systems.

COMPLEX FUNCTION PROJECTIVE SYNCHRONIZATION IN FRACTIONAL-ORDER COMPLEX NETWORKS AND ITS APPLICATION IN FRACTAL PATTERN RECOGNITION

Based on the stability theory of fractional-order systems, a projective synchronization scheme with different coefficients is realized in [Formula: see text] complex networks to build a model for fractal pattern recognition. In the proposed complex function projection synchronization scheme, first a drive-response network is constructed with [Formula: see text] fractional-order complex nodes; And then reasonable controllers are designed to realize the function projection synchronization with different projection coefficients, which are used to encode the fractal pattern; Finally, using the synchronization error system, the input variables for identifying fractal patterns can be solved, and the fractal pattern can be recognized. From the perspective of neurodynamics, the proposed model provides a better understanding of human perception system.

Projective Synchronization of Nonidentical Fractional-Order Memristive Neural Networks

This paper investigates projective synchronization of nonidentical fractional-order memristive neural networks (NFMNN) via sliding mode controller. Firstly, based on the sliding mode control theory, a new fractional-order integral sliding mode controller is designed to ensure the occurrence of sliding motion. Furthermore, according to fractional-order differential inequalities and fractional-order Lyapunov direct method, the trajectories of the system converge to the sliding mode surface to carry out sliding mode motion, and some sufficient criteria are obtained to achieve global projective synchronization of NFMNN. In addition, the conclusions extend and improve some previous works on the synchronization of fractional-order memristive neural networks (FMNN). Finally, a simulation example is given to verify the effectiveness and correctness of the obtained results.

Projective synchronization via feedback controller of fractional-order chaotic systems

ABSTRACT This paper presents a type of fractional-order chaotic systems with fractional order greater than one, on which the projective synchronization via feedback controller has been applied. Through literal presumptions, the projective synchronization is approached. To validate the efficiency of the suggested scheme, the considered systems have been simulated. The simulations have been performed by using Matlab.

Improved Results on Adaptive Control Approach for Projective Synchronization of Neural Networks with Time-Varying Delay

Abstract Compared to other types of synchronization such as complete synchronization and lag synchronization, there is a unique advantage in projective synchronization since it can greatly improve the security of communication. In this paper, the projective synchronization problem of a class of chaotic neural networks with time-varying delay is investigated via designing a novel adaptive controller. Some simple and useful criteria are derived by employing Lyapunov functional method and Lagrange mean value theorem. Finally, an example and its numerical simulations are given to demonstrate the effectiveness of the proposed control schemes. It is worth to mention that the designed controller in this paper dos not require any knowledge about the activation functions, which can be seen the main novelty of the paper.

Adaptive projective synchronization for a class of switched chaotic systems

This paper addresses the problem of projective synchronization of chaotic systems and switched chaotic systems by adaptive control methods. First, a necessary and sufficient condition is proposed to show how many state variables can realize projective synchronization under a linear feedback controller for the chaotic systems. Then, accordingly, a new algorithm is given to select all state variables that can realize projective synchronization. Furthermore, according to the results of the projective synchronization of chaotic systems, the problem of projective synchronization of the switched chaotic systems comprised by the unified chaotic systems is investigated, and an adaptive global linear feedback controller with only one input channel is designed, which can realize the projective synchronization under the arbitrary switching law. It is worth mentioning that the proposed method can also realize complete synchronization of the switched chaotic systems. Finally, the numerical simulation results verify the correctness and effectiveness of the proposed method.

Modified Functional Projective Synchronization of the Unidirectional and Bidirectional Hybrid Connective Star Network with Coupling Time-Delay

An unidirectional and bidirectional hybrid connective star network model with coupling time-delay is constructed in this paper. According to synchronization error systems, adaptive controllers for each node are structured by using the linear system stability method and the Lyapunov stability method. These adaptive controllers can realize the modified functional projective synchronization between each node of star network and an isolated node by argument and analysis. Finally, the corrective and effective of the adaptive controllers are illustrated by some numerical examples.

Improved Control Schemes for Projective Synchronization of Delayed Neural Networks with Unmatched Coefficients

Projective synchronization (PS) is a type of chaos synchronization where the states of slave system are scaled replicas of the states of master system. This paper studies the asymptotic projective synchronization (APS) between master–slave chaotic neural networks (NNs) with mixed time-delays and unmatched coefficients. Based on useful inequality techniques and constructing a suitable Lyapunov functional, some simple criteria are derived to ensure the APS of considered networks via designing a novel adaptive feedback controller. In addition, a numerical example and its MATLAB simulations are provided to check the feasibility of the obtained results. The main innovation of our work is that we dealt with the APS problem between two different chaotic NNs, while most of the existing works only concerned with the PS of chaotic systems with the same topologies. In addition, compared with the controllers introduced in the existing papers, the designed controller in this paper does not require any knowledge about the activation functions, which can be seen as another novelty of the paper.

LMI conditions for some dynamical behaviors of fractional-order quaternion-valued neural networks

This paper addresses the issue of three dynamical behaviors including global Mittag-Leffler stability, robust stability and projection synchronization for fractional-order quaternion-valued neural networks (FQVNNs). Some linear matrix inequality conditions for these dynamical behaviors of FQVNNs are given by Lyapunov stability theory, quaternion matrix theory, Homeomorphic mapping theory and fractional differential equation theory. Furthermore, these obtained sufficient conditions for stability and synchronization are superior to those in existing literature. Finally, three examples are given to illustrate the effectiveness of the theoretical results.