Projective Lag Synchronization Research Articles

Lag projective synchronization of discrete-time fractional-order quaternion-valued neural networks with time delays

This paper deals with the lag projective synchronization (LPS) problem for a class of discrete-time fractional-order quaternion-valued neural networks(DTFO QVNNs) systems with time delays. Firstly, a DTFOQVNNs system with time delay is constructed. Secondly, linear and adaptive feedback controllers with sign function are designed respectively. Furthermore, through Lyapunov direct method, DTFO inequality technique and Razumikhin theorem, some sufficiency criteria are obtained to ensure that the system in this article can achieve LPS. At last, the significance of the theoretical part of this paper is verified through numerical simulation.

Novel Results on Fixed-Time Complex Projective Lag Synchronization for Fuzzy Complex-Valued Neural Networks With Inertial Item

Novel Results on Fixed-Time Complex Projective Lag Synchronization for Fuzzy Complex-Valued Neural Networks With Inertial Item

Further results on fixed/preassigned-time projective lag synchronization control of hybrid inertial neural networks with time delays

This article aims to study fixed-time projective lag synchronization(FXPLS) and preassigned-time projective lag synchronization(PTPLS) of hybrid inertial neural networks(HINNs) with state-switched and discontinuous activation functions(DAFs). By constructing new hybrid fixed-time control and based on theory of non-smooth analysis, we achieve novel results on FXPLS for such HINNs. Through designing novel hybrid preassigned-time control, new criteria on PTPLS of the HINNs is also taken into account. And as distinct from recent works, the FXPLS and PTPLS results are established via non-variable substitution and in a more generalized framework than common synchronization, which also has more extensive practical applications. Finally, example simulations are displayed to set forth the validity of the acquired FXPLS and PTPLS.

Global asymptotic stability and projective lag synchronization for uncertain inertial competitive neural networks

In this paper, the global asymptotic stability and projective lag synchronization of second‐order competitive neural networks with mixed time‐varying delays and uncertainties are studied without converting the original system into the usual first‐order system. Firstly, according to the Lyapunov functional method, inequality technique and the designed adaptive control strategy, the algebraic criteria of stability, and projective lag synchronization are derived by adjusting the control gain parameters in the controller. The obtained sufficient conditions are simple and easy to verify. Different from the traditional feedback controller, the adaptive controller can adjust its characteristics according to the system model, and external disturbance makes the system have better control performance. Besides, unlike the existing ones, this stability and synchronization problem is directly analyzed by constructing some new Lyapunov functionals with state variables and state variable derivatives. Finally, the effectiveness and practicability of the results are verified by numerical examples.

Finite-time lag projective synchronization of delayed fractional-order quaternion-valued neural networks with parameter uncertainties

This paper discusses a class issue of finite-time lag projective synchronization (FTLPS) of delayed fractional-order quaternion-valued neural networks (FOQVNNs) with parameter uncertainties, which is solved by a non-decomposition method. Firstly, a new delayed FOQVNNs model with uncertain parameters is designed. Secondly, two types of feedback controller and adaptive controller without sign functions are designed in the quaternion domain. Based on the Lyapunov analysis method, the non-decomposition method is applied to replace the decomposition method that requires complex calculations, combined with some quaternion inequality techniques, to accurately estimate the settling time of FTLPS. Finally, the correctness of the obtained theoretical results is testified by a numerical simulation example.

Finite-time lag projective synchronization of nonidentical fractional delayed memristive neural networks

Without considering identical systems, this paper investigates the finite-time lag projective synchronization of nonidentical fractional delayed memristive neural networks (FDMNN) by designing a novel fractional sliding mode controller (SMC). Due to the existence of memristor, the research is under the framework of Filippov solution. We firstly construct a fractional integral sliding mode surface (SMS). Based on sliding mode control theory and Lyapunov stability theorem, a novel fractional SMC is proposed to realize the lag projective synchronization of nonidentical FDMNN in finite time, and the synchronization setting time is less conservative than the existing results. As the special cases, some sufficient conditions are extended to projective synchronization, lag synchronization, anti-lag synchronization of nonidentical FDMNN in finite time, which improve and enrich some existing results. At last, a simulation example is given to prove the validity of the conclusions.

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.

Lag projective synchronization of nonidentical fractional delayed memristive neural networks

In this paper, lag projective synchronization of nonidentical fractional delayed memristive neural networks (NFDMNN) is investigated. Due to the existence of memristor, the analysis is based on the theory of differential equations with discontinuous right-hand side proposed by Filippov. A novel controller with fractional integral sliding-mode surface is devised firstly. Successively, some sufficient criteria ensuring lag projective synchronization of NFDMNN are obtained, depending on the fractional calculus inequalities and Lyapunov direct method. Moreover, the related results improve and enrich previous synchronization works. Lastly, the validity of conclusions is verified through a simulation example.

A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

Projective-lag synchronization of complex systems has attracted much attention in the past two decades. However, the majority of previous studies concentrated on continuous-time chaotic systems or discrete-time chaotic systems with the same dimensions. In our present study, a general method for projective-lag synchronization of different discrete-time chaotic systems characterized with different dimensions is first demonstrated. On the basis of stability theory of discrete-time dynamical systems and Lyapunov stability theory, general controllers are designed by using the active control method. The method could achieve projective-lag synchronization in both cases: and . The effectiveness and feasibility of the proposed method is demonstrated by the projective-lag synchronization between two-dimensional Lorenz discrete-time system and three-dimensional Stefanski map, as well as between the three-dimensional generalized Hénon map and the two-dimensional quadratic map, respectively.

Reliable mode-dependent memorized projective lag synchronization for semi-Markovian jumping coupled networks

This article investigates the reliable projective lag synchronization problem for semi-Markovian jumping coupled networks under the master–slave framework. More precisely, a novel mode-dependent memorized synchronization scheme is proposed for the master and slave dynamical networks. By utilizing the Lyapunov-Krasovskii method, sufficient delay-dependent conditions are derived to achieve the reliable synchronization in the mean-square sense. Based on the derived results, the mode-dependent synchronization controller is further designed by convex optimization. In the end, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

Finite-Time Projective Lag Synchronization and Identification between Multiple Weights Markovian Jumping Complex Networks with Stochastic Perturbations

Two nonidentical dimension Markovian jumping complex networks with stochastic perturbations are taken as objects. The network models under two conditions including single weight and double weights are established, respectively, to study the problem of synchronization and identification. A finite-time projection lag synchronization method is proposed and the unknown parameters of the network are identified. First of all, based on Itô’s formula and the stability theory of finite-time, a credible finite-time adaptive controller is presented to guarantee the synchronization of two nonidentical dimension Markovian jumping complex networks with stochastic perturbations under both conditions. Meanwhile, in order to identify the uncertain parameters of the network with stochastic perturbations accurately, some corresponding sufficient conditions are given. Finally, numerical simulations under two working conditions are given to demonstrate the effectiveness and feasibility of the main theory result.

Projective–lag synchronization scheme between two different discrete-time chaotic systems

This paper addresses theoretical analysis of projective–lag synchronization between two different discrete-time chaotic systems. We overcome some limitations of previous works where projective–lag synchronization can only be achieved in continuous-time chaotic systems. In this paper, we realize projective–lag synchronization in discrete-time chaotic systems with the same order. Based on the Lyapunov stability theory and a nonlinear control scheme, the controllers are designed by using the relevant variables of master and slave systems, and we find sufficient conditions for the stability of the error dynamics. The correctness of theoretical analysis is verified by 2D and 3D discrete-time chaotic systems, respectively.

Robust modified function projective lag synchronization between two nonlinear complex networks with different-dimensional nodes and disturbances

This paper is concerned with a theoretical investigation on the robust modified function projective lag synchronization (MFPLS) between two complex networks with nonlinear couplings, different-dimensional nodes, parameter disturbances and external disturbances. Some novel robust hybrid controllers are designed to address such synchronization problems for networks with and without disturbances, in which adaptive updated laws of disturbances are adopted to attenuate the disturbances occurred in networks. By utilizing Lyapunov functional method, synchronization criteria are derived by strict theoretical proof. Compared with existing jobs, the proposed model and synchronization type are more general. Two examples are presented to verify our results.

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.

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.

Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays

AbstractThis paper addresses Master–Slave synchronization for some memristor‐based fractional‐order BAM neural networks (MFBNNs) with mixed time varying delays and switching jumps mismatch. Firstly, considering the inherent characteristic of FMNNs, a new type of fractional‐order differential inequality is proposed. Secondly, an adaptive switching control scheme is designed to realize the global projective lag synchronization goal of MFBNNs in the sense of Riemann‐Liouville derivative. Then, based on a suitable Lyapunov method, under the framework of set‐valued map, differential inclusions theory, fractional Barbalat's lemma and proposed control scheme, some new projective lag synchronization criteria for such MFBNNs are obtained. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed theoretical analysis.

Lag projective synchronization of fractional-order delayed chaotic systems

This paper considers the lag projective synchronization of fractional-order delayed chaotic systems. The lag projective synchronization is achieved through the use of comparison principle of linear fractional equation at the presence of time delay. Some sufficient conditions are obtained via a suitable controller. The results show that the slave system can synchronize the past state of the driver up to a scaling factor. Finally, two different structural fractional order delayed chaotic systems are considered in order to examine the effectiveness of the lag projective synchronization. Feasibility of the proposed method is validated through numerical simulations.

A general formula of complex synchronizations with complex scaling diagonal matrix and time lag

Abstract In this paper, we show a novel sort of complex synchronization. We call this sort complex modified projective lag synchronization (CMPLS). CMPLS, which is a broader instance of synchronizations, is hardly studied or not mentioned till date. We study it to a framework, with certain or uncertain parameters, of two chaotic complexes n-dimensional owing to chaotic attractors with similar structure direct parts yet differing absolutely or mostly in nonlinear terms. In view of the Lyapunov work with lag in time an approach plans are intended to accomplish CMPLS for such matches of complex frameworks with certain or indeterminate parameters. Logical expressions for the complex control capacity are determined to utilize these plans to accomplish CMPLS. This kind of complex synchronization is considered as a speculation of many sorts of synchronizations and complex synchronizations that have shown up in the current writing. The frameworks in CMPLS can be synchronized using an unpredictable scale diagonal lattice. The viability of the obtained results is represented by concentrating two cases of such coupled chaotic attractors with certain or indeterminate parameters in the complex domain. We can plot the numerical results to clear errors frameworks, modulus errors and phase errors of chaotic attractors and that can be after synchronization to show that CMPLS is accomplished.

Projective lag synchronization of different fractional order chaotic systems based on parameter identification

Projective lag synchronization (LPS) of two different structural fractional order hyperchaotic systems with unknown parameters is investigated. The stability theorem of fractional order linear systems is the basis of designing a scheme of LPS and parameter updating laws. Finally, the method is successfully applied to realize LPS and parameter identification between fractional order hyperchaotic system and fractional order hyperchaotic system, and numerical simulations illustrate the effectiveness of the obtained results.

Finite-time generalized projective lag synchronization criteria for neutral-type neural networks with delay

In this paper, we mainly investigate the finite-time generalized projective lag synchronization of neutral-type neural network with delay. With the help of the definition of finite-time generalized projective lag synchronization and Gronwall–Bellman inequality, the generalized projective lag synchronization is achieved between drive-response neural networks via a nonlinear feedback controller. Some novel and easily verifiable sufficient conditions are obtained. Many existing works can be regarded as special cases of our conclusions. Finally, we provide two simulation examples to verify the correctness of main results.