Projective Synchronization Scheme Research Articles

Chaos Controllability in Non-Identical Complex Fractional Order Chaotic Systems via Active Complex Synchronization Technique

In this paper, we primarily investigate the methodology for the hybrid complex projective synchronization (HCPS) scheme in non-identical complex fractional order chaotic systems via an active complex synchronization technique (ACST). Appropriate controllers of a nonlinear type are designed in view of master–slave composition and Lyapunov’s stability criterion (LSC). The HCPS is an extended version of the previously designed projective synchronization scheme. In the HCPS scheme, by using a complex scale matrix, the system taken as slave system is asymptotically synchronized with another system taken as the master system. By utilizing a complex scale matrix, the unpredictability and security of communication are increased along with image encryption. An efficient computational method has been employed to validate and visualize the HCPS method’s efficacy by performing numerical simulation outcomes in MATLAB (version 2021).

Controlling hyperchaos in non-identical systems using active controlled hybrid projective combination-combination synchronization technique

The current manuscript investigates a hybrid projective combination-combination synchronization scheme (HPCCSS) in four different hyperchaotic (HC) systems via active control technique (ACT). In view of Lyapunov stability theory (LST), the discussed strategy determines asymptotic stability globally. Also, numerous synchronization schemes, namely, projective synchronization, chaos control issue, combined synchronization, and many more turn into specific kinds for combination-combination (C-C) synchronization. Also, a comparison analysis within the given HPCCSS and prior published literature has been done. The proposed scheme has applications in secure communication as well as encryption. Additionally, numerical simulation is executed to check the efficiency of considered scheme using MATLAB software.

Controlling and synchronization in chaotic systems using parameter identification method

In this manuscript, we investigate projective synchronization (PS) between identical chaotic new Hamiltonian systems based on Henon-Heiles Model using parameter identification method (PIM). Initially, Lyapunov’s ´ theory of stability is used to design the proper adaptive controllers in view of master-slave configuration to achieve the global asymptotic stability. Also, the proposed technique establishes identification of parameter simultaneously via PS scheme. Additionally, numerical simulations are performed using MATLAB software for visualizing the efficiency and feasibility of the proposed methodology. Furthermore, the discussed approach has numerous significant applications in encryption and secure communication.

Hybrid Projective Synchronization of 4-D Hyperchaotic Systems via Adaptive Control

This paper designs a procedure for investigating the hybrid projective synchronization (HPS) scheme between two identical 4-D hyperchaotic systems. Based on Lyapunov stability theory (LST), an adaptive control technique (ACT) has been designed to achieve the desired HPS scheme. The suggested technique determines globally the asymptotic stability and identification of parameters simultaneously using HPS scheme. It is noted that complete , hybrid and anti-synchronization turns into particular cases of HPS scheme. Numerical simulations are presented to validate the effectivity and feasibleness of the considered technique by using MATLAB. Remarkably, the theoretical and computational outcomes are in complete agreement. Also, the considered HPS scheme is very efficient as it has numerous applications in encryption and secure communication.

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.

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.

A Novel Adaptive Active Control Projective Synchronization of Chaotic Systems

This paper investigates adaptive active control projective synchronization scheme. A general synchronization controller and parameter update laws are proposed to stabilize the error system for the identical structural chaotic systems. It is the first time that the active synchronization, the projective synchronization, and the adaptive synchronization are combined to achieve the synchronization of chaotic systems, which extend the control capability of achieving chaotic synchronization. By using a constant diagonal matrix, the active control is developed. Especially, when designing the controller, we just need to ensure that the diagonal elements of the diagonal matrix are less than or equal 0. So, the synchronization of chaotic systems can be realized more easily. Furthermore, by proposing an active controller, in combination with several different control schemes, we lower the complexity of the design process of the controller. More importantly, the larger the absolute value of product of the diagonal elements of diagonal matrix is, the smoother the curve of chaotic synchronization is and the shorter the time of chaotic synchronization is. In our paper, we take Lorenz system as an example to verify the effectiveness of the proposed synchronization scheme. Theoretical analysis and numerical simulations demonstrate the feasibility of this control method.

Generalized projective series synchronization between chaotic systems and its application

The existence of generalized projective series synchronization scheme between different chaotic systems is investigated. The synchronization scheme consists of three 3D systems and one 4D system to show the generalized projective series synchronization. The synchronization can be well implemented with non-linear adaptive coupling. Sufficient conditions for synchronization are also derived according to Lyapunov stabilization theory. Numerical simulations show the effectiveness of the analytical result. The application of generalized projective series synchronization scheme is implemented to image encryption. The correlation between adjacent pixels in original image and encrypted image is analyzed to show the effectiveness of the synchronization scheme.

A fractional-order form of a system with stable equilibria and its synchronization

There has been an increasing interest in studying fractional-order chaotic systems and their synchronization. In this paper, the fractional-order form of a system with stable equilibrium is introduced. It is interesting that such a three-dimensional fractional system can exhibit chaotic attractors. Full-state hybrid projective synchronization scheme and inverse full-state hybrid projective synchronization scheme have been designed to synchronize the three-dimensional fractional system with different four-dimensional fractional systems. Numerical examples have verified the proposed synchronization schemes.

Active backstepping control of combined projective synchronization among different nonlinear systems

ABSTRACTIn this article, the authors have studied combination projective synchronization using active backstepping method. The main contribution of this effort is realization of the projective synchronization between two drive systems and one response system. We relax some limitations of previous work, where only combination complete synchronization has been investigated. According to Lyapunov stability theory and active backstepping design method, the corresponding controllers are designed to observe combination projective synchronization among three different classical chaotic systems, i.e. the Lorenz system, Rössler system and Chen system. The numerical simulation examples verify the effectiveness of the theoretical analysis. Combination projective synchronization has stronger anti-attack ability and anti-translated ability than the normal projective synchronization scheme realized by one drive and one response system in secure communication.

Hidden attractors without equilibrium and adaptive reduced-order function projective synchronization from hyperchaotic Rikitake system

By introducing an additional state feedback into classic Rikitake system, a new hyperchaotic system without equilibrium is derived. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincare maps. Based on adaptive control and Lyapunov stability theory, we design a reduced-order projective synchronization scheme for synchronizing the hyperchaotic Rikitake system coexisting without equilibria and the original classic Rikitake system coexisting with two non-hyperbolic equilibria. Finally, numerical simulations are given to illustrate the effectiveness of the proposed synchronization scheme.

On a function projective synchronization scheme for non-identical Fractional-order chaotic (hyperchaotic) systems with different dimensions and orders

Referring to fractional-order systems, this paper investigates the inverse full state hybrid function projective synchronization (IFSHFPS) of non-identical systems characterized by different dimensions and different orders. By taking a master system of dimension n and a slave system of dimension m, the method enables each master system state to be synchronized with a linear combination of slave system states, where the scaling factor of the linear combination can be any arbitrary differentiable function. The approach presents some useful features: i) it enables commensurate and incommensurate non-identical fractional-order systems with different dimension n<m or n>m to be synchronized; ii) it can be applied to a wide class of chaotic (hyperchaotic) fractional-order systems for any differentiable scaling function; iii) it is rigorous, being based on two theorems, one for the case n<m and the other for the case n>m. Two different numerical examples are reported, involving chaotic/hyperchaotic fractional-order Lorenz systems (three-dimensional and four-dimensional master/slave, respectively) and hyperchaotic/chaotic fractional-order Chen systems (four-dimensional and three-dimensional master/slave, respectively). The examples clearly highlight the capability of the conceived approach in effectively achieving synchronized dynamics for any differentiable scaling function.

A generalized function projective synchronization scheme for uncertain chaotic systems subject to input nonlinearities

In this paper, a modified generalized function projective synchronization scheme for a class of master–slave chaotic systems subject to dynamic disturbances and input nonlinearities (dead-zone and sector nonlinearities) is investigated. This synchronization system can be seen as a generalization of many existing projective synchronization schemes (namely the function projective synchronization, the modified projective synchronization and so on), in the sense that the master system has a scaling function matrix and the slave system has a scaling factor matrix. To practically achieve this generalized function synchronization, an adaptive fuzzy variable-structure control system is designed. The fuzzy systems are used to appropriately approximate the uncertain nonlinear functions. A Lyapunov approach is employed to prove the boundedness of all signals of the closed-loop control system as well as the exponential convergence of the synchronization errors to an adjustable region. Simulations results are presented to illustrate the effectiveness of the proposed generalized function PS scheme.

Generalized Function Projective Combination-Combination Synchronization of Chaos in Third Order Chaotic Systems

In this paper, a generalized function projective combination-combination synchronization scheme (GFPCCS) among four chaotic systems is investigated via the active backstepping technique. To validate the proposed GFPCCS, suitable controllers are designed via the active backstepping technique to achieve GFPCCS among four chaotic Josephson junctions evolving from different initial conditions. The numerical simulations carried out show the achievement and effectiveness of the GFPCCS for the four chaotic Josephson junctions via the active backstepping technique. The results show that different types of synchronization can be achieved from the GFPCCS based on the choice of the scaling parameters, hence the GFPCCS could be used to modify the behaviour of coupled systems.

Projective Synchronization of Chaotic Discrete Dynamical Systems via Linear State Error Feedback Control

A projective synchronization scheme for a kind of n-dimensional discrete dynamical system is proposed by means of a linear feedback control technique. The scheme consists of master and slave discrete dynamical systems coupled by linear state error variables. A kind of novel 3-D chaotic discrete system is constructed, to which the test for chaos is applied. By using the stability principles of an upper or lower triangular matrix, two controllers for achieving projective synchronization are designed and illustrated with the novel systems. Lastly some numerical simulations are employed to validate the effectiveness of the proposed projective synchronization scheme.

Adaptive hybrid projective synchronization of two coupled fractional-order complex networks with different sizes

This paper investigates a new hybrid projective synchronization scheme between two coupled fractional-order complex networks with different sizes. The hybrid projective synchronization studied in this paper includes complete synchronization of the states of the nodes in each network and projective synchronization of the states of a pair of nodes from both networks. Based on the stability theorem of fractional-order differential system and adaptive control technique, some sufficient conditions for guaranteeing the existence of the hybrid projective synchronization are derived. Two examples are given to show the effectiveness of the proposed methods.

A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems

In this paper, a projective synchronization problem of master–slave chaotic systems is investigated. More specifically, a fuzzy adaptive controller is investigated for a projective synchronization of uncertain multivariable chaotic systems. The adaptive fuzzy-logic systems are used to approximate the unknown functions. A decomposition property of the control gain matrix is used in the controller design and the stability analysis. A Lyapunov approach is employed to derive the parameter adaptation laws and prove the boundedness of all signals of the closed-loop system as well as the exponential convergence of the synchronization errors to an adjustable region. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.

Hybrid Dislocated Control and General Hybrid Projective Dislocated Synchronization for Memristor Chaotic Oscillator System

Some important dynamical properties of the memristor chaotic oscillator system have been studied in the paper. A novel hybrid dislocated control method and a general hybrid projective dislocated synchronization scheme have been realized for memristor chaotic oscillator system. The paper firstly presents hybrid dislocated control method for stabilizing chaos to the unstable equilibrium point. Based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization has been studied for the drive memristor chaotic oscillator system and the same response memristor chaotic oscillator system. For the different dimensions, the memristor chaotic oscillator system and the other chaotic system have realized general hybrid projective dislocated synchronization. Numerical simulations are given to show the effectiveness of these methods.

Weak Projective Synchronization in Drive-Response Dynamical Networks with Time-Varying Delay and Parameter Mismatch

This paper investigates the problem of projective synchronization in drive-response dynamical networks (DRDNs) with time-varying delay and parameter mismatch via impulsive control. Owing to projective factor and parameter mismatch, complete projective synchronization cannot be achieved. Therefore, a weak projective synchronization scheme is proposed to ensure that the DRDNs are in a state of synchronization with an error level. Based on the stability analysis of the impulsive functional differential equations, a general method of the weak projective synchronization with the error level is derived in DRDNs. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results.

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

In this paper, we investigate adaptive switched generalized function projective synchronization between two new different hyperchaotic systems with unknown parameters, which is an extension of the switched modified function projective synchronization scheme. Based on the Lyapunov stability theory, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve adaptive switched generalized function projective synchronization between two different hyperchaotic systems. A numerical simulation is conducted to illustrate the validity and feasibility of the proposed synchronization scheme.