Delayed Reaction-diffusion Neural Networks Research Articles

TSSD-based quasi-synchronization of stochastic delayed reaction–diffusion neural networks under deceptional attacks

The quasi-synchronization (QS) issue of stochastic delayed reaction–diffusion neural networks (SDRDNNs) under deceptive attacks is investigated in this paper. A control strategy in terms of time-space sampled-data (TSSD) is presented for the QS issue of SDRDNNs under deceptive attacks, which can not only enhance the cybersecurity of communications but also reduce network bandwidth consumption. By looped Lyapunov–Krasovskii functional (LKF), free-weighting matrix (FWM) technique, second-order B-L integral inequality, Itô’s formula, generalized Itô’s isometry, Dynkin’s formula and the extended Halanay’s inequality, a newly less conservative QS criterion is established for SDRDNNs under norm-bounded deceptive attacks. Furthermore, to increase the feasibility of the QS criterion, by the total expectation formula and independent increment of Brownian motion, an innovative and effective method for estimating the mathematical expectation of the dw(t)dt-dependent cross-term in the corresponding FWM-based zero equation is proposed. Additionally, this study also develops the TSSD exponential synchronization (ES) criteria for SDRDNNs without deceptive attacks and for SDRDNNs under deceptive attacks with Bernoulli distribution. Finally, a simulated example consisting of three cases is provided to validate the feasibility and effectiveness of the theoretical results.

Event-triggered synchronization for delayed reaction–diffusion neural networks under hybrid deception attacks

This paper focuses on designing some event-triggered mechanisms to synchronize the delayed reaction–diffusion neural networks (DRDNNs) under hybrid stochastic deception attacks. Firstly, two different kinds of stochastic deception attacks are considered for DRDNNs system. Based on the distinct characteristics of the attack signals, a novel adaptive event-triggered control mechanism is proposed to synchronize DRDNNs under hybrid deception attacks subject to Lipschitz form, and a novel aperiodic event-triggered control mechanism is proposed to synchronize DRDNNs under hybrid deception attacks subject to bounded form. Using the Lyapunov theory and some inequality techniques, several event-triggered synchronization criteria for DRDNNs under hybrid deception attacks are established. Furthermore, Zeno behavior is strictly excluded by proving the existence of lower bounds for the intervals between any adjacent events in the two designed event-triggered mechanisms. Finally, two numerical examples are provided to illustrate the effectively and superiority of the two proposed event-triggered mechanisms.

Novel Caputo fractional differential approach and hybrid control scheme for finite‐time synchronization of nonidentical delayed reaction–diffusion neural networks

AbstractThis work focuses on the finite‐time synchronization (F‐TS) for nonidentical delayed neural networks (DNNs) including Caputo fractional partial differential operator and reaction–diffusion terms. A novel F‐TS lemma is proposed by constructing a new Caputo differential inequality. Applying the new lemma and designing two hybrid controllers with time delay and the sign function, the F‐TS criteria on the introduced Caputo reaction–diffusion nonidentical DNNs under the Neumann boundary condition are derived by making use of the Filippov differential inclusion, Green's theorem, and fractional Razumikhin theorem. The conditions are expressed through the algebraic inequality which can greatly decrease the computation in checking the F‐TS performance. Moreover, the validity and correctness of the F‐TS results are illustrated by selecting various orders, spatial positions, and diffusion parameters.

Synchronization of reaction–diffusion neural networks with random time-varying delay via intermittent boundary control

Under boundary measurement (BM), this paper solves the synchronization problem via intermittent boundary proportional–derivative (PD) control of delayed reaction–diffusion neural networks (RDNNs), where the random time-varying delay (RTVD) belongs to two intervals and is considered by a probabilistic way to take the influence of uncertain factors. The intermittent boundary PD synchronization scheme, which considers the inevitable actuator limitations, is based on BM and only available at some specified boundary position. By using the inequality techniques and switching Lyapunov functional, the mean square exponential stability (MSES) of the synchronization error system (SES) containing the response and drive dynamics is ensured by some synchronization criteria, which are established via an intermittent boundary PD controller under BM and expressed as linear matrix inequalities. Lastly, the proposed intermittent boundary PD synchronization approach is verified by a numerical example.

Intermittent State Observer Design for Neural Networks With Reaction–Diffusion Terms Using Partial Measurements

This article develops a novel state observer for delayed reaction–diffusion neural networks by utilizing incomplete measurements. To reduce the transmission cost efficiently, the space domain is divided into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L$</tex-math> </inline-formula> parts and only partial information needs to be measured in every subdomain, such as a point in one-dimensional space, a line and a plane in two-and three-dimensional space, respectively. In addition, the time domain is divided: the measured output signals are transmitted intermittently. Then, new conditions that assure the asymptotic stability of observation error system are derived based on the Lyapunov direct method and several inequality techniques. Finally, the proposed approach’s effectiveness is demonstrated via three numerical examples.

Adaptive event-triggered extended dissipative synchronization of delayed reaction–diffusion neural networks under deception attacks

Under spatially averaged measurements (SAMs) and deception attacks, this article mainly studies the problem of extended dissipativity output synchronization of delayed reaction–diffusion neural networks via an adaptive event-triggered sampled-data (AETSD) control strategy. Compared with the existing ETSD control methods with constant thresholds, our scheme can be adaptively adjusted according to the current sampling and latest transmitted signals and is realized based on limited sensors and actuators. Firstly, an AETSD control scheme is proposed to save the limited transmission channel. Secondly, some synchronization criteria under SAMs and deception attacks are established by utilizing Lyapunov–Krasovskii functional and inequality techniques. Then, by solving linear matrix inequalities (LMIs), we obtain the desired AETSD controller, which can satisfy the specified level of extended dissipativity behaviors. Lastly, one numerical example is given to demonstrate the validity of the proposed method.

Intermittent Boundary Control for Synchronization of Fractional Delay Neural Networks With Diffusion Terms

This article studies the synchronization of new coupled fractional delayed reaction–diffusion neural networks with reaction terms satisfying the global Lipschitz condition via time-continuous and time-discontinuous boundary controllers. The realization of neural networks inevitably involves diffusion phenomena and time delays, and all the neurons of neural networks are interrelated. Considering these aspects, this study focuses on coupled fractional neural networks with time-delay and diffusion terms. A state-dependent boundary control (BC) is designed for when the state information is available, and a criterion is presented to ensure the synchronization of the considered systems. Considering the advantages of a time-discontinuous controller, an intermittent BC and a criterion of synchronization are given. When the state information cannot be fully obtained, a boundary-output-based observer is provided for estimating the states. Then, an observer-based intermittent boundary controller is given to ensure the synchronization. From the given criteria, the effects of time delay and the control time length on synchronization are analyzed. This research involves two key challenges: 1) consideration of the BC and intermittent control parameters in the system performance analysis and 2) clarification of the influence of system parameters on synchronization. These challenges are addressed using Poincaré’s inequality, the fractional Razumikhin-type theorem, and several properties of the Mittag-Leffler function are used to deal with the above difficulties. Examples show that our results are valid.

Asymptotic Behavior of Delayed Reaction-Diffusion Neural Networks Modeled by Generalized Proportional Caputo Fractional Partial Differential Equations

In this paper, a delayed reaction-diffusion neural network model of fractional order and with several constant delays is considered. Generalized proportional Caputo fractional derivatives with respect to the time variable are applied, and this type of derivative generalizes several known types in the literature for fractional derivatives such as the Caputo fractional derivative. Thus, the obtained results additionally generalize some known models in the literature. The long term behavior of the solution of the model when the time is increasing without a bound is studied and sufficient conditions for approaching zero are obtained. Lyapunov functions defined as a sum of squares with their generalized proportional Caputo fractional derivatives are applied and a comparison result for a scalar linear generalized proportional Caputo fractional differential equation with several constant delays is presented. Lyapunov functions and the comparison principle are then combined to establish our main results.

Global synchronization for BAM delayed reaction-diffusion neural networks with fractional partial differential operator

This paper is devoted to the exploration of the global asymptotic synchronization (GAS) and global Mittag–Leffler synchronization (GMLS) issues on bidirectional associative memory reaction-diffusion neural networks (BAMRDNNs), which include a Caputo’s fractional partial differential operator, leakage and discrete delays. By means of the Green’s theorem, Jensen’s integral inequality and Lyapunov functional approach, several synchronization criteria are established by using the hybrid controllers. The presented results are described in the algebraic inequalities form, which can immensely reduce the computational complexity. Moreover, these results reveal the impact of the network system coefficient matrices on GAS and GMLS. Finally, in the three-dimensional space, the effectiveness and practicability of these synchronization criteria are confirmed by choosing different derivative orders and diffusion coefficients.

Event-triggered passivity and synchronization of coupled reaction–diffusion neural networks with and without time-varying delay

This paper is devoted to deal with the event-triggered passivity and synchronization problems for two types of coupled reaction–diffusion neural networks (CRDNNs). In the first type, several passivity and synchronization criteria for CRDNNs are acquired through designing suitable event-triggered controllers, combining some inequality techniques and Lyapunov functional approach. In the second type, the problems of event-triggered synchronization and passivity for coupled delayed reaction–diffusion neural networks (CDRDNNs) are investigated. Finally, two numerical examples are provided to illustrate the effectiveness of the derived passivity and synchronization conditions.

Asymptotic stability of singular delayed reaction-diffusion neural networks

Asymptotic stability of singular delayed reaction-diffusion neural networks

Input-to-state stability of delayed reaction-diffusion neural networks with multiple impulses

<abstract> This paper concerns the input-to-state stability problem of delayed reaction-diffusion neural networks with multiple impulses. After reformulating the neural-network model in term of an abstract impulsive functional differential equation, the criteria of input-to-state stability are established by the direct estimate of mild solution and an integral inequality with infinite distributed delay. It shows that the input-to-state stability of the continuous dynamics can be retained under certain multiple impulsive disturbance and the unstable continuous dynamics can be stabilised by the multiple impulsive control, if the intervals between the multiple impulses are bounded. The numerical simulation of two examples is given to show the effectiveness of theoretical results. </abstract>

Passivity Analysis of Markov Jumping Delayed Reaction-Diffusion Neural Networks under Different Boundary Conditions

This work analyzes the passivity for a set of Markov jumping reaction-diffusion neural networks limited by time-varying delays under Dirichlet and Neumann boundary conditions, respectively, in which Markov jumping is used to describe the variations among system parameters. To overcome some difficulties originated from partial differential terms, the Lyapunov–Krasovskii functional that introduces a new integral term is proposed and some inequality techniques are also adopted to obtain the delay-dependent stability conditions in terms of linear matrix inequalities, which ensures that the designed neural networks satisfy the specified performance of passivity. Finally, the advantages and effectiveness of the obtained results are verified via displaying two illustrated examples.

Resilient fault-tolerant anti-synchronization for stochastic delayed reaction–diffusion neural networks with semi-Markov jump parameters

This paper deals with the anti-synchronization issue for stochastic delayed reaction–diffusion neural networks subject to semi-Markov jump parameters. A resilient fault-tolerant controller is utilized to ensure the anti-synchronization in the presence of actuator failures as well as gain perturbations, simultaneously. Firstly, by means of the Lyapunov functional and stochastic analysis methods, a mean-square exponential stability criterion is derived for the resulting error system. It is shown the obtained criterion improves a previously reported result. Then, based on the present analysis result and using several decoupling techniques, a strategy for designing the desired resilient fault-tolerant controller is proposed. At last, two numerical examples are given to illustrate the superiority of the present stability analysis method and the applicability of the proposed resilient fault-tolerant anti-synchronization control strategy, respectively.

General decay synchronization and [formula omitted] synchronization of spatial diffusion coupled delayed reaction–diffusion neural networks

This paper deals with the general decay synchronization (GDS) and general decay H∞ synchronization (GDHS) problems for spatial diffusion coupled delayed reaction–diffusion neural networks (SDCDRDNNs) without and with uncertain parameters respectively. First, based on the ψ-type stability and ψ-type function, the concept of GDS is generalized to include general robust decay synchronization (GRDS) and GDHS. Then, by exploiting a nonlinear controller and different types of inequality techniques, some verifiably sufficient conditions ensuring the GDS and GDHS of SDCDRDNNs (without and with uncertain parameters) are derived. Finally, two simulative examples are provided to demonstrate the validity of the synchronization results obtained.

Quantized Sampled-Data Synchronization of Delayed Reaction-Diffusion Neural Networks Under Spatially Point Measurements.

This article considers the synchronization problem of delayed reaction-diffusion neural networks via quantized sampled-data (SD) control under spatially point measurements (SPMs), where distributed and discrete delays are considered. The synchronization scheme, which takes into account the communication limitations of quantization and variable sampling, is based on SPMs and only available in a finite number of fixed spatial points. By utilizing inequality techniques and Lyapunov-Krasovskii functional, some synchronization criteria via a quantized SD controller under SPMs are established and presented by linear matrix inequalities, which can ensure the exponential stability of the synchronization error system containing the drive and response dynamics. Finally, two numerical examples are offered to support the proposed quantized SD synchronization method.

Passivity and Synchronization of Coupled Different Dimensional Delayed Reaction-Diffusion Neural Networks with Dirichlet Boundary Conditions

Two types of coupled different dimensional delayed reaction-diffusion neural network (CDDDRDNN) models without and with parametric uncertainties are analyzed in this paper. On the one hand, passivity and synchronization of the raised network model with certain parameters are studied through exploiting some inequality techniques and Lyapunov stability theory, and some adequate conditions are established. On the other hand, the problems of robust passivity and robust synchronization of CDDDRDNNs with parameter uncertainties are solved. Finally, two numerical examples are given to testify the effectiveness of the derived passivity and synchronization conditions.

Adaptive stochastic synchronization of delayed reaction–diffusion neural networks

In this paper, we deal with the adaptive stochastic synchronization for a class of delayed reaction–diffusion neural networks. By combing Lyapunov–Krasovskii functional, drive-response concept, the adaptive feedback control scheme, and linear matrix inequality method, we derive some sufficient conditions in terms of linear matrix inequalities ensuring the stochastic synchronization of the addressed neural networks. The output coupling with delay feedback and the update laws of parameters for adaptive feedback control are proposed, which will be of significance in the real application. The novel Lyapunov–Krasovskii functional to be constructed is more general. The derived results depend on the measure of the space, diffusion effects, and the upper bound of derivative of time-delay. Finally, an illustrated example is presented to show the effectiveness and feasibility of the proposed scheme.

Employing the Friedrichs’ inequality to ensure global exponential stability of delayed reaction-diffusion neural networks with nonlinear boundary conditions

By employing the Friedrichs’ inequality and M-matrices, we have obtained two sets of sufficient conditions to ensure global exponential stability of the reaction-diffusion Hopfield networks with S-type distributed delays and nonlinear boundary conditions. Our work demonstrates that both diffusion effects, boundary conditions and shapes of spatial regions have played critical roles in determining the global exponential stability of the network system. Comparing with the previous work, our method can further provide how to find the more accurate and larger convergence rate. We also present several examples and simulations of the network models defined respectively on the cylinder, unit ball, cube and line segment so as to show the significance and application of our theory. The theoretical result and the idea here can be applied in considering system control and synchronization with or without random terms.

Impulsive synchronization of two coupled delayed reaction–diffusion neural networks using time-varying impulsive gains

In this paper, the problem of impulsive synchronization of two coupled delayed reaction–diffusion neural networks under aperiodic discrete measurements is revisited. Different from the previous static impulsive gain based impulsive synchronization strategy, a novel impulsive synchronization strategy using sampling-interval-dependent impulsive gains is proposed. The time-varying impulsive synchronization gains are able to adapt to the variation of sampling intervals, and thus can improve the synchronization performance. The stability analysis of the resultant synchronization error system is performed by applying an impulse-time-dependent discretized Lyapunov functions based method. Sufficient conditions for the existence of desired impulsive synchronization controllers are derived in terms of a set of linear matrix inequalities (LMIs). These conditions allow to synthesize time-varying impulsive gains. A numerical example is presented to demonstrate the effectiveness of the developed methodology.