Synchronization Of Complex-valued Neural Networks Research Articles

Fixed-time synchronization of complex-valued neural networks for image protection and 3D point cloud information protection

This paper studies the fixed-time synchronization (FDTS) of complex-valued neural networks (CVNNs) based on quantized intermittent control (QIC) and applies it to image protection and 3D point cloud information protection. A new controller was designed which achieved FDTS of the CVNNs, with the estimation of the convergence time not dependent on the initial state. Our approach divides the neural network into two real-valued systems and then combines the framework of the Lyapunov method to give criteria for FDTS. Applying synchronization to image protection, the image will be encrypted with a drive system sequence and decrypted with a response system sequence. The quality of image encryption and decryption depends on the synchronization error. Meanwhile, the depth image of the object is encrypted and then the 3D point cloud is reconstructed based on the decrypted depth image. This means that the 3D point cloud information is protected. Finally, simulation examples verify the efficacy of the controller and the synchronization criterion, giving results for applications in image protection and 3D point cloud information protection.

Sliding Mode Control-Based Synchronization of Complex-Valued Neural Networks

Sliding Mode Control-Based Synchronization of Complex-Valued Neural Networks

Global synchronization of complex-valued neural networks with unbounded time-varying delays

This paper investigates global synchronization of complex-valued neural networks (CVNNs) with unbounded time-varying delays. By applying analytical method and inequality techniques, an algebraic criterion is established to ensure global synchronization of the CVNNs via a devised feedback controller, which generalizes some existing outcomes. Finally, two numerical simulations and one application in image encryption are provided to verify the effectiveness of the theoretical results.

A novel intermittent sliding mode control approach to finite-time synchronization of complex-valued neural networks

In this work, the issue of finite-time synchronization is discussed for complex-valued neural networks (CVNNs) by applying aperiodically intermittent sliding mode control and a non-separation approach. Firstly, to simplify the theoretical analysis process, some new differential inequalities are established, and new estimated time rules are given. Secondly, to avoid the traditional approach of separating CVNNs, a novel complex-valued aperiodically intermittent sliding mode control strategy is designed, which has never been applied to achieve CVNNs synchronization. Furthermore, by adopting the newly established lemmas, novel controllers and Lyapunov functional, some novel finite-time synchronization criteria of CVNNs are acquired. At last, the validity of the resulting conclusions is indicated by some numerical examples.

Stability and synchronization for complex-valued neural networks with stochastic parameters and mixed time delays.

In this paper, a class of complex-valued neural networks (CVNNs) with stochastic parameters and mixed time delays are proposed. The random fluctuation of system parameters is considered in order to describe the implementation of CVNNs more practically. Mixed time delays including distributed delays and time-varying delays are also taken into account in order to reflect the influence of network loads and communication constraints. Firstly, the stability problem is investigated for the CVNNs. In virtue of Lyapunov stability theory, a sufficient condition is deduced to ensure that CVNNs are asymptotically stable in the mean square. Then, for an array of coupled identical CVNNs with stochastic parameters and mixed time delays, synchronization issue is investigated. A set of matrix inequalities are obtained by using Lyapunov stability theory and Kronecker product and if these matrix inequalities are feasible, the addressed CVNNs are synchronized. Finally, the effectiveness of the obtained theoretical results is demonstrated by two numerical examples.

Event-based master–slave synchronization of complex-valued neural networks via pinning impulsive control

This paper investigates the synchronization problem of complex-valued neural networks via event-triggered pinning impulsive control (ETPIC). A time-delayed pinning impulsive controller is proposed based on three levels of event-triggered conditions. By employing the Lyapunov functional method and differential inequality technique, sufficient delay-dependent synchronization criteria are derived under the proposed ETPIC scheme. The obtained result shows that synchronization of master and slave complex-valued neural networks can be achieved even if the sizes of delays exceed the length of intervals between any two consecutive impulsive instants determined by Lyapunov-based event-triggered conditions in the proposed control strategy. Moreover, the linear matrix inequality approach is utilized to exclude Zeno behavior. Numerical examples are provided to illustrate the effectiveness of the theoretical results.

The Module-Phase Synchronization of Complex-Valued Neural Networks with Time-Varying Delay and Stochastic Perturbations

The Module-Phase Synchronization of Complex-Valued Neural Networks with Time-Varying Delay and Stochastic Perturbations

Effects of heterogeneous impulses on synchronization of complex-valued neural networks with mixed time-varying delays

This article investigates a new type of impulsive effect, namely the heterogeneous impulsive effect on the synchronization of complex-valued neural networks (CVNNs) with mixed time-varying delays. Heterogeneous impulsive effect is a unified framework of non-identical and time-varying impulses, i.e., the impulsive effect to state of each neuron is not only non-identical to each other but also distinct at different impulsive times. Here heterogeneous impulsive control is designed, which is an extension of hybrid impulsive control. The problem is studied with the following procedures. Firstly, the master–slave CVNNs are explicitly separated into two real-valued neural networks (RVNNs). Secondly, the two RVNNs are transformed into impulsive error dynamical system using the heterogeneous impulsive controller. Thirdly, the concepts of average impulsive interval (AII) and average impulsive gain (AIG) are implemented to obtain the synchronization of delayed CVNNs under heterogeneous impulsive effects. By employing a matrix measure method and extended impulsive Halanay inequality, sufficient criteria are derived to guarantee exponential synchronization of the given delayed CVNNs. The dependency of convergence rates on AIIs and AIGs is explicitly discussed. Finally, two examples are provided to show the efficiency of the proposed theoretical results.

Matrix Measure Approach for Stability and Synchronization of Complex-Valued Neural Networks with Deviating Argument

This paper concentrates on global exponential stability and synchronization for complex-valued neural networks (CVNNs) with deviating argument by matrix measure approach. The Lyapunov function is no longer required, and some sufficient conditions are firstly obtained to ascertain the addressed system to be exponentially stable under different activation functions. Moreover, after designing a suitable controller, the synchronization of two complex-valued coupled neural networks is realized, and the derived condition is easy to be confirmed. Finally, some numerical examples are given to demonstrate the superiority and feasibility of the presented theoretical analysis and results.

Exponential Synchronization of Complex-Valued Neural Networks Via Average Impulsive Interval Strategy

In this paper, the issue of the exponential synchronization for complex-valued neural networks with both discrete and distributed delays is investigated by applying impulsive control protocol. Based on the Lyapunov–Krasovskii function, average impulsive interval as well as the comparison principle, some simple verifiable sufficient criteria are established to guarantee the exponential synchronization between the master and the slave systems. Meanwhile, through the serious analysis of the networks systems, the exponential convergence rate can be specified. Additionally, a numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

Quasi-projective synchronization of stochastic complex-valued neural networks with time-varying delay and mismatched parameters

This paper aims to study the issue of stochastic quasi-projective synchronization of complex-valued neural networks with time-varying delays in the case of the simultaneous existence of parameter mismatch and stochastic disturbance. Instead of separating the real and imaginary parts, by constructing a suitable controller, a quasi-projective synchronization criterion of two nonidentical systems is established by combining the complex version It’s formula with some inequality techniques in the framework of complex domain. Meanwhile, the bound of synchronization error is estimated. Some sufficient conditions for special cases are also presented. Finally, the effectiveness of the obtained results are verified by a numerical example.

Finite-time synchronization of complex-valued neural networks with finite-time distributed delays

This paper is dedicated to addressing the issue of the finite-time synchronization of complexed-valued neural networks with finite-time distributed delays. Some results are derived for finite-time synchronization of the drive-response system using the new Lyapunov–Krasovskii function and the analysis techniques. We then propose several numerical examples to determine the effectiveness of the results.

Synchronization of Coupled Complex-Valued Impulsive Neural Networks with Time Delays

In this paper, we mainly investigate synchronization of complex-valued neural networks (CVNNs) with time delays and impulsive effects. By using Lyapunov method and some inequality techniques, some sufficient conditions for the synchronization of CVNNs with time delays and impulsive effects are proposed. Finally, a numerical example based on small-world networks is presented to demonstrate correctness of the theoretical results.

Global Synchronization of Complex-Valued Neural Networks With Stochastic Disturbances and Time-Varying Delay

This paper discusses synchronization problem of two delayed stochastic neural networks. By constructing the Lyapunov functions, using stochastic analysis technique, some sufficient conditions guaranteeing the synchronization in mean square for the drive system with the response system have been derived in terms of linear matrix inequalities (LMIs) approach. Moreover, the main feature of this paper lies in that the present results are applicable for the drive system and the response system which all are considered not only in complex-valued domain but also with stochastic noise case. Two numerical examples are given to illustrate the effectiveness and merits of the present results.

Synchronization of complex-valued neural networks with mixed two additive time-varying delays

This paper focus on the synchronization of complex-valued neural networks (CVNNs) with both discrete and distributed two additive time-varying delays. By applying matrix inequality technique and exploiting reciprocally convex approach, several delay-dependent criteria are presented in the form of linear matrix inequalities (LMIs) to ensure the global synchronization of CVNNs via structuring an appropriate Lyapunov–Krasovskii functional. An example with simulations is provided to ensure the feasibility of the obtained result.

Finite-Time Synchronization of Complex-Valued Neural Networks with Multiple Time-Varying Delays and Infinite Distributed Delays

This paper investigates finite-time synchronization of complexed-valued neural networks with multiple time-varying delays and infinite distributed delays. By separating the complex-valued neural networks into the real and the imaginary parts, the corresponding equivalent real-valued systems are obtained. Some sufficient conditions are derived for finite-time synchronization of the drive-response system based on the new Lyapunov–Krasovskii function and the new analysis techniques. Numerical examples demonstrate the effectiveness of the theoretical results.

Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks

In this paper, without separating the complex-valued neural networks into two real-valued systems, the quasi-projective synchronization of fractional-order complex-valued neural networks is investigated. First, two new fractional-order inequalities are established by using the theory of complex functions, Laplace transform and Mittag-Leffler functions, which generalize traditional inequalities with the first-order derivative in the real domain. Additionally, different from hybrid control schemes given in the previous work concerning the projective synchronization, a simple and linear control strategy is designed in this paper and several criteria are derived to ensure quasi-projective synchronization of the complex-valued neural networks with fractional-order based on the established fractional-order inequalities and the theory of complex functions. Moreover, the error bounds of quasi-projective synchronization are estimated. Especially, some conditions are also presented for the Mittag-Leffler synchronization of the addressed neural networks. Finally, some numerical examples with simulations are provided to show the effectiveness of the derived theoretical results.

Global Exponential Synchronization of Complex-Valued Neural Networks with Time Delays via Matrix Measure Method

In this paper, global exponential synchronization of a class of complex-valued neural networks with time delays is investigated. Based on Halanay inequality theory, Lyapunov theory and matrix measure method, by separating complex-valued neural networks to the real part and imaginary part, several criteria for the global exponentially synchronization of complex-valued neural networks are presented. Finally, one numerical simulation is given to show the effectiveness of our theoretical results.

Finite-Time Synchronization of Complex-Valued Neural Networks with Mixed Delays and Uncertain Perturbations

This paper concerns the problem of finite-time synchronization for a class of complex-valued neural networks (CVNNs) with both time-varying and infinite-time distributed delays (mixed delays). Both the driving and response CVNNs are disturbed by external uncertain perturbations, which may be nonidentical. A simple state-feedback controller is designed such that the response CVNNs can be synchronized with the driving system in a settling time. By using inequality techniques and constructing some new Lyapunov---Krasovskii functionals, several sufficient conditions are derived to ensure the synchronization. It is discovered that the settling time cannot be estimated when the interested CVNNs exhibit infinite-time distributed delays, while it can be explicitly estimated for the CVNNs with bounded delays. The settling time is dependent on both the delays and the initial value of the error system. Finally, numerical simulations demonstrate the effectiveness of the theoretical results.

具有泄漏时滞的复值神经网络的全局同步性

The global synchronization of complex-valued neural networks with leakage time delays was investigated. For the considered complex-valued neural networks, the activation functions need not be separated into real parts and imaginary parts. Through the construction of appropriate Lyapunov-Krasovskii functionals, with the drive-response synchronization method, the free-weighting matrix method and the matrix inequality technique, a delay-dependent criterion for checking the global synchronization of complex-valued neural networks with leakage time delays was established in the form of complex-valued linear matrix inequality (LMI), meanwhile the design method for the synchronization controllers was given. Finally, a simulation example shows the effectiveness of the present work.