Function Projective Synchronization Research Articles

Finite-time and fixed-time function projective synchronization of competitive neural networks with noise perturbation

Finite-time and fixed-time function projective synchronization of competitive neural networks with noise perturbation

Generalized function projective synchronization of identical and nonidentical chaotic systems

Generalized function projective synchronization of identical and nonidentical chaotic systems

Control and adaptive modified function projective synchronization of a new chaotic system

Control and adaptive modified function projective synchronization of a new chaotic system

Function projective Mittag-Leffler synchronization of non-identical fractional-order neural networks

This article investigates the function projective Mittag-Leffler synchronization (FPMLS) between non-identical fractional-order neural networks (FONNs). The stability analysis is carried out using an existing lemma for the Lyapunov function in the FONN systems. Based on the stability theorem of FONN, a non-linear controller is designed to achieve FPMLS. Moreover, global Mittag-Leffler synchronization (GMLS) is investigated in the context of other synchronization techniques, such as projective synchronization (PS), anti-synchronization (AS) and complete synchonization (CS). Using the definition of the Caputo derivative, the Mittag-Leffler function and the Lyapunov stability theory, some stability results for the FPMLS scheme for FONN are discussed. Finally, the proposed technique is applied to a numerical example to validate its efficiency and the unwavering quality of the several applied synchronization conditions.

Combined modified function projective synchronization of different systems through adaptive control

Combined modified function projective synchronization of different systems through adaptive control

Generalized Function Projective Synchronization of Two Different Chaotic Systems with Uncertain Parameters

This study proposes a new approach to realize generalized function projective synchronization (GFPS) between two different chaotic systems with uncertain parameters. The GFPS condition is derived by converting the differential equations describing the synchronization error systems into a series of Volterra integral equations on the basis of the Laplace transform method and convolution theorem, which are solved by applying the successive approximation method in the theory of integral equations. Compared with the results obtained by constructing Lyapunov functions or calculating the conditional Lyapunov exponents, the uncertain parameters and the scaling function factors considered in this paper have fewer restrictions, and the parameter update laws designed for the estimation of the uncertain parameters are simpler and easier to realize physically.

Adaptive fixed-time robust control for function projective synchronization of hyperchaotic economic systems with external perturbations

In today's sophisticated world, where financial systems play an increasingly important role, the application of controllers through management strategies is of crucial importance, given their vital role. An analysis of the synchronization of economic systems can provide a valuable insight into the financial synchronous development of different countries or regions around the world. In this paper, an adaptive fixed-time control strategy is presented for the function projective synchronization of drive-response hyperchaotic economic systems with unknown parameters and external perturbations. The developed controller is constructed by combining the fixed-time control approach and parametric adaptation technique. Specifically, the adaptive adjusting mechanisms are designed to estimate the unknown parameters and external perturbations, respectively. Stability investigation shows that the function projective synchronization errors under the developed controller can stabilize to the minor fields about zero in fixed time. A key feature of the developed controller is its high insensitive to unknown parameters and strong robustness against external perturbations. Finally, the effectiveness and merits of the presented control strategy are examined by simulation scenarios.

A new adaptive iterative learning control of finite-time hybrid function projective synchronization for unknown time-varying chaotic systems

A new adaptive iterative learning control (AILC) scheme is proposed to solve the finite-time hybrid function projective synchronization (HFPS) problem of chaotic systems with unknown periodic time-varying parameters. Fourier series expansion (FSE) is introduced to deal with the problem of uncertain time-varying parameters. The bound of the expanded remaining items is unknown. A typical convergent series is used to deal with the unknown bound in the design process of the controller. The adaptive iterative learning synchronization controller and parameter update laws are designed. Two different chaotic systems are synchronized asymptotically according to different proportional functions on a finite time interval by Lyapunov stability analysis. The simulation example proves the feasibility and effectiveness of the proposed method.

Control and adaptive modified function projective synchronization of different hyperchaotic dynamical systems

<abstract><p>In this work, we consider an adaptive control method, which is simpler and generalized to obtain some conditions on the parameters for hyperchaotic models determined by using a Lyapunov direct method. Further, an adaptive controller for synchronization is designed by using Lyapunov functions by which the deriving system and the response system can realize adaptive modified function projective synchronization up to scaling matrix. Numerical simulation of each system is discussed in detail with graphical results. The graphical results are presented in detail in order to validate the theoretical results. These results in this article generalize and improve the corresponding results of the recent works.</p></abstract>

Dislocated function projective partial synchronization between dynamical systems

By generalizing the classical Lorenz chaotic system, we construct the n-dimension and m-dimension dynamical systems as the drive system and response one respectively. And then we present the definitions of the dislocated function projective partial synchronization (DFPPS) and general dislocated function projective partial synchronization (GDFPPS) between the two dynamical systems. Based on Lyapunov stability theorem the controllers to realize DFPPS and GDFPPS of the two dynamical systems can be obtained in indeterminate equations. We find that no matter what dynamical behaviors the two systems have, their DFPPS and GDFPPS can be realized by controlling to partial variables (even one variable) of the response system. Three numerical examples are presented to illustrate the correctness and effectiveness of the studied results. Simultaneously, in the process of realizing GDFPPS of systems, it is important that we get a pair of more complicated time series about chaotic synchronization.

Function Projective Synchronization of Two Complex Networks with Unknown Sector Nonlinear Input and Multiple Time-Varying Delay Couplings

This paper deals with the function projective synchronization of two complex dynamic networks with unknown sector nonlinear input, multiple time-varying delay couplings, model uncertainty, and external interferences. Based on Lyapunov stability theory and inequality transformation method, the robust adaptive synchronization controller is designed, by which the drive and response systems can achieve synchronization according to the function scaling factor. Different from some existing studies on nonlinear system with sector nonlinear input, this paper studies the synchronization of two complex dynamic networks when the boundary of sector nonlinear input is unknown. The controller does not include the boundary value of the sector nonlinear input and the time delay term, so it is more practical and relatively easy to implement. The corresponding simulation examples demonstrate the effectiveness of the proposed scheme.

Dissipative Pinning Sampled-Data Control for Function Projective Synchronization of Neural Networks With Hybrid Couplings and Time-Varying Delays

This paper is concerned with the dissipative problem based pinning sampled-data control scheme. We investigate the problem for function projective synchronization of neural networks with hybrid couplings and time-varying delays. The main purpose is focused on designing a pinning sampled-data function projective synchronization controller such that the resulting function projective synchronization neural networks are stable and satisfy a strictly H∞,L2 - L∞, passivity and dissipativity performance by setting parameters in the general performance index. It is assumed that the parameter uncertainties are norm-bounded. By construction of an appropriate Lyapunov-Krasovskii containing single, double and triple integrals, which fully utilize information of the neuron activation function and use refined Jensen’s inequality for checking the passivity of the addressed neural networks are established in linear matrix inequalities (LMIs). This result is less conservative than the existing results in literature. It can be checked numerically using the effective LMI toolbox in MATLAB. Numerical examples are provided to demonstrate the effectiveness and the merits of the proposed methods.

Function Projective Synchronization between Two Discrete-Time Hyperchaotic Systems Using Backstepping Method

We realize the function projective synchronization (FPS) between two discrete-time hyperchaotic systems, that is, the drive state vectors and the response state vectors can evolve in a proportional scaling function matrix. In this paper, a systematic scheme is explored to investigate the function projective synchronization of two identical discrete-time hyperchaotic systems using the backstepping method. Additionally, FPS of two different hyperchaotic systems is also realized. Numeric simulations are given to verify the effectiveness of our scheme.

Complex Modified Function Projective Lag Synchronization With Fixed-Time Stability Guarantees for Hyperchaotic Systems via a Fixed-Time Control Proposal

Our paper investigates complex modified function projective lag synchronization with fixed-time stability guarantees for hyperchaotic systems via a FxTC proposal. The synchronization of complex hyperchaotic systems and the desired performance are definitely guaranteed within a period of bounded time. The synchronization interval can be predefined without demanding the information of the initial conditions from the systems where the synchronization is performed. Furthermore, the fixed-time stability guarantees of the control scheme are achieved according to the Lyapunov principle and the settling time is calculated by solving the differential equations. In MATLAB/SIMULINK environment, synchronization performance from two simulation examples is performed in many cases with the change of initial values and time delay of the system to reveal the feasibility and the efficacy of the control proposal.

Modified function projective synchronization of master-slave neural networks with mixed interval time-varying delays via intermittent feedback control

<abstract><p>The modified function projective synchronization problem for master-slave neural networks with mixed interval time-varying delays is presented using periodically intermittent feedback control. The interval distributed time-varying delay including the lower and upper bound is comprehensively established, which developed from the previous work. The following techniques are utilize to analyze the appropriate criteria for the modified function projective synchronization problem for master-slave neural networks with mixed interval time-varying delays such as the construction of appropriate Lyapunov-Krasovskii functionals merged with Newton-Leibniz formulation method, the intermittent feedback control technique, the reciprocally convex technique's lower bound lemma, Jensen's inequality, and the piecewise analytic method. The sufficient criteria for the modified function projective synchronization of the error system between the master and slave neural networks with intermittent feedback control are first established in terms of linear matrix inequalities (LMIs). The designed controller ensures that the synchronization of the error systems are proposed via intermittent feedback control. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method.</p></abstract>

Bursting mechanism in a memristive Lorenz based system and function projective synchronization in its-fractional-order form: Digital implementation under ATmega328P microcontroller

In this paper, bifurcation mechanism of bursting oscillations and function projective synchronization of the fractional order form for a memristive Lorenz based system are investigated. One of the key results is the dependance of relaxation time of bursting oscillation on the fractional order derivative. The newly proposed system has a line equilibrium and accordingly, features hidden attractors. When the system is divided into two subsystems labeled slow subsystem(SS) and fast subsystem(FS), stability analysis indicates that bursting oscillations result from the switching of the equilibrium point of the(FS) between stable and unstable states. We refer this class of bursting as ”source/bursting”. The second aspect of this paper deals with the study of fractional order of the system precisely function projective synchronization in a relay topology. By using some standard nonlinear diagnostic tools such as bifurcation diagram, largest Lyapunov exponent, phase space trajectory and power spectrum, the study of the fractional model reveals that the dynamics strongly depends on system parameters , fractional order q as well as on initial conditions. With a set of chosen parameters , the proposed scheme achieves function projective synchronization in a finite time despite the unpredictability of the scaling function. The Results of digital implementation based on a ATmega328P microcontroller are in good agreement with those found by numerical simulations.

The Switching Function Projective Synchronization Dynamics of two Distinct Van der Pol-Duffing Oscillators with a Memristor-Duffing Oscillator

In this paper, through the discontinuous dynamical system theory, the system interactions of two distinct Van der Pol-Duffing oscillators and a Memristor-Duffing oscillator is discussed under a switching nonlinear controller with symbolic functions. The interaction conditions of three chaotic systems are treated as separation boundaries which is time-varying. Thus the corresponding motion domains are constrained by the boundaries and studied, and the analytical conditions for function project synchronization of three nonautonomous system via the switch-ability and attractivity of edge flows are developed. The control parameter maps with different invariant sets are also studied under the analytical conditions. The partial and full function projective synchronization are carried out via numerical simulations, and the interactions of the control parameters on the synchronization has been investigated. The switching projective synchronization are experimentally realized via analog circuit, and the experimental results validate the theoretical analysis.

Dynamics and synchronization of the complex simplified Lorenz system

In this paper, the complex simplified Lorenz system is proposed. It is the complex extension of the simplified Lorenz system. Dynamics of the proposed system is investigated by theoretical analysis as well as numerical simulation, including bifurcation diagram, Lyapunov exponent spectrum, phase portraits, Poincaré section, and basins of attraction. The results show that the complex simplified Lorenz system has non-trivial circular equilibria and displays abundant and complicated dynamical behaviors. Particularly, the coexistence of infinitely many attractors, i.e., extreme multistability, is discovered in the proposed system. Furthermore, the adaptive complex generalized function projective synchronization between two complex simplified Lorenz systems with unknown parameter is achieved. Based on Lyapunov stability theory, the corresponding adaptive controllers and parameter update law are designed. The numerical simulation results demonstrate the effectiveness and feasibility of the proposed synchronization scheme. It provides a theoretical and experimental basis for the applications of the complex simplified Lorenz system.

Analysis and modified function projective synchronization of integer and fractional-order autonomous Morse jerk oscillator

Dynamical analysis and modified function projective synchronization (MFPS) of integer and fractional-order Morse jerk oscillator are investigated in this paper. Integer-order Morse jerk oscillator generates periodic behaviors, periodic spiking and two different shapes of chaotic attractors. The periodic spiking and chaotic behaviors obtained during numerical simulations of integer-order Morse jerk oscillator is ascertained by using electronic implementation. The numerical simulations results qualitatively agree with the Orcad-PSpice results. Moreover, MFPS of identical and mismatched chaotic Morse jerk oscillators is numerically investigated. At last, the theoretical investigation of fractional-order Morse jerk oscillator reveals the existence of chaos in Morse jerk oscillator for order greater or equal to 2.85.

Control and adaptive modified function projective synchronization of a new hyperchaotic system

The purpose of this investigation is the applications of the feedback control method in order to control the behavior of the new hyperchaotic system. We consider hyperchaotic system first and then apply the feedback control method to obtain the results for the control of the hyperchaotic system. We present some conditions on the parameters values and show that the controlled system is stable which is established by the Routh–Hurwitz criterion. We also show results for the adaptive modified function projective synchronization (AMFPS) of two identical new hyperchaotic systems with known parameters. Using the Lyapunov stability theory, we can present the system that the is asymptotically stable. At last, we provide numerical results for the justifications of the theoretical results by considering the initial values of the variables and the suitable parameters values. The simulated results justify the importance of the considered method.