Reaction-diffusion Terms Research Articles

Fixed-Time Synchronization for Delayed Quaternion-Valued Stochastic Fuzzy Neural Network with Reaction–Diffusion Terms

Fixed-Time Synchronization for Delayed Quaternion-Valued Stochastic Fuzzy Neural Network with Reaction–Diffusion Terms

A phase field-based systematic multiscale topology optimization method for porous structures design

In this paper, we propose a novel and systematic phase field-based multiscale topology optimization method for porous structures design. The multi-regional microstructural composite and fixed microstructural shapes are adopted to balance the objective and other constraints. The connectivity issue between different microstructures is handled. In the multiscale topology optimization, the macro and micro design variables are updated by the Allen-Cahn type equations which include a reaction-diffusion term, a sensitivity analysis term, a volume constraint term, and a correction term. The correction term is used to keep topologies of macro and micro structures closed to the prescribed structures. We use an efficient merging algorithm to handle the connectivity issue between different microstructures. Based on an interpolation technique of the phase field function and a modified Allen-Cahn equation, this algorithm can smooth the connecting boundaries and satisfy the minimum surface theorem. The final distribution of microstructures keeps the extraordinary physical and mechanical properties for the macrostructure. Some typical cantilever beam, Michell-type structure and Messerschmitt-Bölkow-Blohm beam are performed to verify the effectiveness of our method.

Anti-disturbance synchronization of fuzzy genetic regulatory networks with reaction-diffusion

This paper intends to focus on the anti-disturbance synchronization issue for genetic regulatory networks subject to reaction-diffusion terms based on the Takagi-Sugeno fuzzy model. In view of the fact that disturbances are widespread in actual control engineering, the stability of the aforementioned systems would be affected, therefore, ensuring the stability of closed-loop genetic regulatory networks is the main goal of this paper. The unknown disturbances are supposed to be generated by an exogenous system, which can be estimated by developing disturbance observers. Furthermore, integrating the disturbance observers with fuzzy rule-based conventional control laws, a new anti-disturbance control strategy is proposed to reject the disturbances and guarantee the desired dynamic performances. Then, by constructing a proper Lyapunov function and using advanced decoupling techniques, some sufficient conditions in the form of linear matrix inequalities, to guarantee the asymptotic stability of the error system, are obtained. Finally, an illustrated example is presented to demonstrate the effectiveness and superiority of the proposed method.

Switching synchronization of reaction-diffusion neural networks with time-varying delays

This paper explores the switching synchronization problem of reaction-diffusion neural networks with time-varying delays, and two improved synchronization switching law strategies are proposed for stability analysis. One is constructed by adopting a Lyapunov-Krasovskii functional combined with the use of improved Wirtinger's integral inequality for managing the reaction-diffusion terms. The other is designed to utilize the Lyapunov-Razumikhin function, which is easier to deal with the reaction-diffusion terms directly compared to the former one. As a result, the time-space feature of the proposed switching synchronization is more robust and compatible than previous works. Finally, the simulated numerical experiments make out the effectiveness of the developed approaches in this work.

Space-Dividing-Based Cluster Synchronization of Reaction-Diffusion Genetic Regulatory Networks via Intermittent Control.

In this paper, we focus on the cluster synchronization of reaction-diffusion genetic regulatory networks (RDGRNs) with time-varying delays, where the state of the system is not only time-dependent but also spatially-dependent due to the presence of the reaction-diffusion terms. First, we construct an intermittent space-dividing controller that effectively combines the two control strategies, making it more cost-effective. Furthermore, based on the activation function division approach, we propose a regulation function division method that can improve the delay upper bound of RDGRNs; meanwhile, the cluster synchronization criteria of RDGRNs under the proposed controller are derived based on the Lyapunov theory and Halanay's et al. inequality techniques. Finally, the criteria's effectiveness is demonstrated by numerical examples of the system in one- and two-dimensional space.

Event-triggered [formula omitted]/passive synchronization for Markov jumping reaction–diffusion neural networks under deception attacks

The issue of H∞/passive master–slave synchronization for Markov jumping neural networks with reaction–diffusion terms is investigated in this paper via an event-triggered control scheme under deception attacks. To lighten the burden of limited communication bandwidth as well as ensure the control performance, an event-triggered transmission scheme is developed. Meanwhile, the randomly occurring deception attacks, which received from the event generator are assumed to modify the sign of the control signal, are taken into account. Furthermore, sufficient conditions ensuring the prescribed H∞/passive performance level of the neural networks, are deduced beyond Lyapunov stability theory, and the controller gains are derived dealing with the matrix convex optimization problem. At last, the availability of the approach proposed is demonstrated via a numerical example.

Exponential state estimation for reaction-diffusion inertial neural networks via incomplete measurement scheme

ABSTRACT In this paper, the problem of exponential state estimation for inertial neural networks with reaction-diffusion term (RDINNs) via incomplete measurement scheme is investigated. Unlike the full measurement method, this method estimates the system by measuring the state of partially available neurons. First, by constructing an appropriate variable substitution, the second-order system is transformed into a first-order one. Then, a suitable Lyapunov-krasovskii function (LKF) is constructed, and sufficient conditions for the stability of the system are obtained . Finally, the practicality and effectiveness of the proposed method is further verified by two numerical examples.

Synchronization of multiple neural networks with reaction–diffusion terms under cyber–physical attacks

In this paper, we investigate the synchronization problem of multiple neural networks with reaction–diffusion terms under cyber–physical attacks via distributed control. As for the multiagent systems, designing security control laws for multiple neural networks (MNNs) with reaction–diffusion terms is a big challenge when the proposed neural networks perform various cooperative tasks under failures or attacks. In complex environment, the MNNs with reaction–diffusion terms may be under mixed attacks, and one of them has been named cyber–physical attacks which would affect the communication links and nodes leading to the change of topology and states, as well as the distributed controllers. To deal with these issues, we will construct a novel Lyapunov function and combine with some properties of M-matrix to investigate the effects caused by cyber–physical attacks, and a security control law is also given to ensure the synchronization of the proposed neural network system. On the algorithmic side, it is worth mentioning that the security architecture and the security control algorithm are given to choose parameters of the feedback gain matrix and the coupling strength to achieve synchronization. Finally, a numerical simulation is given to support the obtained theoretical results.

Synchronization in Finite/Fixed Time for Markovian Complex-Valued Nonlinear Interconnected Neural Networks With Reaction–Diffusion Terms

This paper considers a novel class of nonlinear interconnected neural networks (INNs) where the Markovian jump parameters and reaction–diffusion terms are both involved. The nonlinear INNs are studied in the complex domain, which is a meaningful attempt in the research on INNs. Then, by designing a suitable nonlinear controller and employing the Lyapunov functional and algebraic inequality technologies, a finite/fixed-time synchronization criterion in probability can be obtained for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> subsystems. Note that the criteria for synchronization in finite time and fixed time are obtained with only one controller and integrated into a unified theorem. A secret communication example is presented, such that the validity and practicability of this paper can be verified.

Anti-synchronization of delayed memristive neural networks with leakage term and reaction–diffusion terms

In this paper, the global exponential anti-synchronization problem is studied for an array of delayed memristive neural networks (DMNNs) with leakage term and reaction–diffusion terms. Firstly, to investigate the exponential anti-synchronization problems, we will design two different types of controllers for the proposed systems. Secondly, via adopting Lyapunov functional method, the drive–response theory and some inequality techniques, several sufficient conditions are obtained to ensure the global exponential anti-synchronization of the proposed DMNNs with leakage term and reaction–diffusion terms. Specifically, the delays could be time-varying or constants in the leakage term. Compared with the previously research results, the proposed neural network models herein are more general, and the obtained results consider the diffusion effects, leakage delay and time-varying delays, and those results can improve and enrich the previously obtained results. At last, two numerical examples are provided to demonstrate the validity of the derived theoretical results.

Synchronization of fractional-order spatiotemporal complex-valued neural networks in finite-time interval and its application

This paper focuses on the synchronization of fractional-order complex-valued neural networks (FOCVNNs) with reaction–diffusion terms in finite-time interval. Different from the existing complex-valued neural networks (CVNNs), the reaction–diffusion phenomena and fractional derivative are first considered into the system, meanwhile, the parameter switching (the system parameters will switch with the state) is considered, which makes the presented model more comprehensive. By choosing an appropriate Lyapunov function, the driver and response systems achieve Mittag-Leffler synchronization under a suitable controller. In addition, based on the fractional calculus theorem and the basic inequality methods, a criterion of synchronization for the error system in finite-time interval is derived and the upper bound of the corresponding finite synchronization time can be obtained. Finally, two examples are provided, one is a numerical example to explain the effectiveness of the main results, and the other shows that the results of this paper can be applied to image encryption for any size with high-security coefficient.

Global Exponential Stability and Periodicity of Nonautonomous Impulsive Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

In this paper, we investigate the global exponential stability and periodicity of nonautonomous cellular neural networks with reaction-diffusion, impulses, and time-varying delays. By establishing a new differential inequality for nonautonomous systems, using the properties of M-matrix and inequality techniques, some new sufficient conditions for the global exponential stability of the system are obtained. Moreover, sufficient conditions for the periodic solutions of the system are obtained by using the Poincare mapping and the fixed point theory. The validity and superiority of the main results are verified by numerical examples and simulations.

Exponential passive filter design for switched neural networks with time-delay and reaction-diffusion terms

This paper investigates the problem of exponential passive filter design for switched neural networks with time-delay and reaction-diffusion terms. With the aid of a suitable Lyapunov–Krasovskii functional and some inequalities, a linear matrix inequality-based design method is developed that not only makes the filtering error system exponentially stable but also forces it to be passive from external interference to output error. Then, the filter design is extended to the complex-valued case via separating the system into real-valued and complex-valued parts. Finally, a numerical example is utilized to illustrate the effectiveness of the filter design methods for the real-valued and complex-valued cases, respectively.

Asymptotical stability of fractional neutral-type delayed neural networks with reaction-diffusion terms

This article investigates the asymptotical stability of the equilibrium point for a class of fractional neutral-type delayed neural networks with reaction-diffusion terms in sense of Riemann–Liouville. In terms of linear matrix inequalities approach, inequality scaling techniques and Green’s theorem, by constructing a suitable Lyapunov functional, some less conservative criterion of asymptotical stability for the neural networks system are given. Inspired by some achievements, the results obtained in this paper are more general and can easily test the stability of practical neural networks systems. Finally, two numerical examples are elaborated to substantiate the validity and conciseness of theoretical results.

Extended dissipative-based state estimation for Markov jump coupled neural networks with reaction-diffusion terms

This work mainly concentrates on the state estimation for Markov jump coupled neural networks (MJCNNs) with reaction-diffusion terms, in which the memory controller is employed. First, the considered MJCNNs model is introduced, and the dynamic error system can be obtained based on the proposed state estimator. Then, a memory controller that involves constant signal transmission delay is designed. Moreover, by Lyapunov functional method, inequality technique and Kronecker product law, a novel stable and extended dissipative analysis criteria can be established to ensure that the stability of the error system the error system. Meanwhile, the controller gains can be obtained by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the developed method.

Aperiodically intermittent pinning outer synchronization control for delayed complex dynamical networks with reaction-diffusion terms

In this paper, we mainly study the outer synchronization problem of complex dynamical networks (CDNs) involving delays and reaction-diffusion terms by aperiodically intermittent pinning control (AIPC). By using piecewise function and Lyapunov-Krasovskii functional method, some criteria for the complete and exponential outer synchronization of the corresponding CDNs with and without the coupling delay are obtained. Furthermore, two numerical examples are provided to illustrate the effectiveness of the obtained results.

Formula omitted] output synchronization of directed coupled reaction-diffusion neural networks via event-triggered quantized control

By designing a quantized controller based on event trigger, this paper considers the problem of H∞ output synchronization for coupled neural networks with reaction-diffusion term and directed topology. Firstly, in this hybrid control strategy, the data is sampled in time domain to exclude the Zeno-behavior before judging whether an event is triggered, and then the event-triggered data instead of the sampling data itself is quantized by a logarithmic quantizer. Secondly, some sufficient conditions for H∞ output synchronization are obtained, in which the dimension of these conditions can be reduced to only depend on the number of neurons, but not on the number of nodes. Finally, a numerical example is given to verify the theoretical results.

Dynamic behaviors for inertial neural networks with reaction-diffusion terms and distributed delays

A class of inertial neural networks (INNs) with reaction-diffusion terms and distributed delays is studied. The existence and uniqueness of the equilibrium point for the considered system is obtained by topological degree theory, and a sufficient condition is given to guarantee global exponential stability of the equilibrium point. Finally, an example is given to show the effectiveness of the results in this paper.

Sampled-Data State Estimation of Reaction Diffusion Genetic Regulatory Networks via Space-Dividing Approaches.

A novel state estimator is designed for genetic regulatory networks with reaction-diffusion terms in this study. First, the diffusion space (where mRNA and protein exist) is divided into several parts and only a point, a line, or a plane, etc., is measured in every subspace to reduce the measurement cost effectively. Then, samplers and network-induced time delay are considered to meet the network transmission requirement. A new criterion to ensure that the estimation error converges to zero is established by using the Lyapunov functional combined with Wirtinger's inequality, reciprocally convex approach, and Halanay's inequality; furthermore, the estimator's parameters are derived by solving linear matrix inequalities. Finally, two simulation examples (including one-dimensional and two-dimensional spaces) are presented to demonstrate the developed scheme's applicability.

Stability analysis of genetic regulatory networks via a linear parameterization approach

This paper investigates the problem of finite-time stability (FTS) for a class of delayed genetic regulatory networks with reaction-diffusion terms. In order to fully utilize the system information, a linear parameterization method is proposed. Firstly, by applying the Lagrange’s mean-value theorem, the linear parameterization method is applied to transform the nonlinear system into a linear one with time-varying bounded uncertain terms. Secondly, a new generalized convex combination lemma is proposed to dispose the relationship of bounded uncertainties with respect to their boundaries. Thirdly, sufficient conditions are established to ensure the FTS by resorting to Lyapunov Krasovskii theory, convex combination technique, Jensen’s inequality, linear matrix inequality, etc. Finally, the simulation verifications indicate the validity of the theoretical results.